WMAP3 and Spatial Closure [Archive]

marcus

Mar10-06, 06:50 PM

Peter Woit called attention to the liklihood that new WMAP data will be coming out soon

for some additional detail here is a post from Anthony Lewis (Cambridge)

http://cosmocoffee.info/viewtopic.php?p=1391#1391

He says that around 23 March there will be one or more conference talks about the Three Year WMAP data. Spergel is one of the principals in WMAP and he is scheduled to give a talk

D. N. Spergel et al. "Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology"

so presumably the data will have to be released by that time.

=================

the last big batch of CMB cosmology data was Bennett et al (2003).

It has been a long time and some people seem to be quite impatient.

The parameter people seem most interested in is Omega and the Bennett 2003 estimate was 1.02 +/- 0.02
this includes the spatially flat case (exactly 1) and also includes the case where space has a slight positive curvature and is presumably finite. (although time is not bounded)

If they could reduce the error-bar and keep the same 1.02, it would send out philosophical shockwaves. For instance if the new data said that Omega is 1.02 +/- 0.01
then it would send out the notion that the universe is not spatially flat but is very slightly positive curved, and that it is spatially finite
and that it will nevertheless keep expanding (at an accelerating rate).

===============

I can't guess anything about the new data, but different results could have impact on people's picture of the universe, and also remember the new data could be exactly the same as the old data and there could be no interesing change too. But the possibilities are just interesting enough so one should keep alert to the forthcoming batch of new data on the CMB

=================
to check out the old data
http://map.gsfc.nasa.gov/m_mm/mr_wmapdata.html

http://map.gsfc.nasa.gov/m_mm/pub_papers/firstyear.html

here is a good one:
http://lambda.gsfc.nasa.gov/

even better:
http://lambda.gsfc.nasa.gov/product/map/current/

their summary of cosmological parameters
http://lambda.gsfc.nasa.gov/product/map/current/wmap_parameters.cfm

Garth

Mar10-06, 06:58 PM

Peter Woit called attention to the liklihood that new WMAP data will be coming out soon

to be precise here is a post from Anthony Lewis (Cambridge)

http://cosmocoffee.info/viewtopic.php?p=1391#1391

He says that around 20-22 March there will be one or more conference talks about the Three Year WMAP data. Spergel is one of the principals in WMAP and he is scheduled to give a talk
20-22 March 2006 or 2007?

Pardon by scepticism! We've been waiting a long time.:wink:

Garth

Mar10-06, 07:08 PM

20-22 March 2006 or 2007?

Pardon by scepticism! We've been waiting a long time.:wink:

:tongue2:
Heard something about that if they don't present any data within the next few months they will have a hard time getting any more funding, so probably they will present at least a piece of it very soon...

SpaceTiger

Mar12-06, 12:01 PM

Yeah, I'm pretty sure the big one is coming. According to David Spergel, some of the papers have been submitted to NASA and the release is now up to them.

marcus

Mar12-06, 03:10 PM

20-22 March 2006 or 2007?

Pardon by scepticism! We've been waiting a long time.:wink:

Garth

:smile:

yes I know we've been waiting a long time

I meant March 2006, in other words in the next week or so
but your skepticism is understandable

wolram

Mar12-06, 03:42 PM

Yeah, I'm pretty sure the big one is coming. According to David Spergel, some of the papers have been submitted to NASA and the release is now up to them.

Why, NASA and not the virgin results ?

SpaceTiger

Mar13-06, 06:16 PM

NASA just announced that the WMAP results will be released this Thursday. You will be able to get the papers and press releases from:

http://lambda.gsfc.nasa.gov/

SpaceTiger

Mar13-06, 06:16 PM

Why, NASA and not the virgin results ?

I'm sorry, I don't understand your question.

Mar13-06, 06:25 PM

NASA just announced that the WMAP results will be released this Thursday.
That's some really exciting news!:smile:

Garth

Mar14-06, 02:45 AM

The parameter people seem most interested in is Omega and the Bennett 2003 estimate was 1.02 +/- 0.02
this includes the spatially flat case (exactly 1) and also includes the case where space has a slight positive curvature and is presumably finite. (although time is not bounded)

If they could reduce the error-bar and keep the same 1.02, it would send out philosophical shockwaves. For instance if the new data said that Omega is 1.02 +/- 0.01
then it would send out the notion that the universe is not spatially flat but is very slightly positive curved, and that it is spatially finite
and that it will nevertheless keep expanding (at an accelerating rate).

===============

I can't guess anything about the new data, but different results could have impact on people's picture of the universe, and also remember the new data could be exactly the same as the old data and there could be no interesing change too. But the possibilities are just interesting enough so one should keep alert to the forthcoming batch of new data on the CMB

=================
That is certainly interesting - it is generally thought that \Omega is just greater than unity already - this release might harden that estimate.

However the most interesting thing for me is whether the quadrupole and other low-l mode deficiencies are confirmed or not and whether an explanation of such a deficiency is offered.

Garth

Chronos

Mar16-06, 02:14 AM

SpaceTiger

Mar16-06, 01:52 PM

I anticipate the results will be hugely complicated and inspire much speculation. I would not at all be surprised that it suggests a spatially finitite universe. The existing data already strongly leans that way.

There's a talk on the results later today. If I have time tonight, I'll make a summary post in this forum.

marcus

Mar16-06, 02:14 PM

I just looked at Spergel et al paper
http://lambda.gsfc.nasa.gov/product/map/dr2/pub_papers/threeyear/parameters/wmap_3yr_param.pdf

Check out figure 20 on page 48
and the caption under figure 21 on page 49

To me it now seems more likely the U is spatially positive curved finite

this is my non-expert take on it and I do not see a relevant error-bar
and there is some balancing and guarded-ness in how they discuss it, which is appropriate, but that is how it looks to me at first sight

hellfire

Mar16-06, 04:27 PM

I took a fast look to the paper and I must say I am a bit disappointed because I was expecting some kind of surprise after the long time we had to wait for these results. I assume that this long time was needed to reach a level of precision on the analysis and conclusions. However, I found not very much information and some vagueness about some issues that I had expected to be treated in detail, such like SZ contamination, ISW and low multipole problem. These are controversial issues that led to alternative models. The paper seams to rely very much on other experiments and it is also repeatedly mentioned the high expectations on future surveys. I assume one has to get used to the fact that current accurate cosmological models are set up like a mosaic, giving us a picture of the whole universe that can be undestood only taking into account all pieces of different precision experiments. This is just my personal opinion after a very fast reading. Let's see what others have to say about it, especially SpaceTiger...

marcus

Mar16-06, 05:46 PM

question to Space Tiger
there is a parameter Omega-sub-K
which they call "spatial curvature"

I do not see this defined anywhere in terms of other parameters.
Also it is not in the corresponding Spergel et al first-year-data paper

could you please define it for us

==================
what puzzles me is that the old estimate of Omega_total seemed to be saying that the U was mostlikely flat (Omega = 1) or nearly flat with a slight positive spatial curvature (like if Omega = 1.01)

Now they have introduced this Omega_k and estimate that it is around -0.015

it seems to me that a NEGATIVE Omega_k is associated with a slight POSITIVE curvature

if this is true it is confusing

So for instance could it be that they have defined Omega_k as follows:

Omega_k = 1 - Omega_total

?

any clarification? thx in advance.

hellfire

Mar16-06, 06:15 PM

Omega_k = 1 - Omega_total
This is right. Take the first Friedmann equation:

H^2 = \frac{8 \pi G}{3c^2} \rho_m - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}

divide by H^2 and you will get:

1 = \Omega_m + \Omega_k + \Omega_{\Lambda}

George Jones

Mar16-06, 06:21 PM

So for instance could it be that they have defined Omega_k as follows:

Omega_k = 1 - Omega_total

?

Yes, this is the curvature "density" - a notational covenience that is often used in cosmology. A c is often used for the subscript k.

Omega_k = - k/(Ha)^2

Regards,
George

marcus

Mar16-06, 09:08 PM

thanks to you both!

marcus

Mar17-06, 01:28 PM

SpaceTiger

Mar17-06, 01:59 PM

So by the definition of Omega_k which,e.g. hellfire gave, we have an estimate of Omega_total

[1.008, 1.037]

so at 68 % confidence the universe is not flat.

instead, at that confidence level, it is positive curve spatial finite.

That's a little deceptive. First of all, the value of the curvature and the error bar are both dependent on which parameters you allow to run free (e.g. we could peg w at -1). It's also dependent on how much information you include. On page 50, table 11 shows the value of \Omega_k one gets after including various other data sets and most of them are consistent with flatness within the 1\sigma error bars.

So I would not say that we're 68% confident the universe is not flat. The data are, of course, consistent with both a closed universe and an open universe as well, but we can't yet distinguish with any confidence. From inflation, we do expect deviations from flatness, but probably not at this level. I think the deviations are expected at the next decimal place.

In interpreting these parameters, it's best to ask whether or not a particular model is consistent with the measurements. The percentage confidence in the value of a particular parameter is model-dependent and depends on error bars that are often crudely approximated. We usually don't take notice of deviations from theory until they're several sigma.

marcus

Mar17-06, 04:44 PM

Any brief statement is apt to be misleading, so let's try to give a more complete picture. I thought about pegging w = -1 too, as you say here.

First of all, the value of the curvature and the error bar are both dependent on which parameters you allow to run free (e.g. we could peg w at -1)...

Pegging w= -1 is easy to do visually from figure 17. Just draw an horizontal line across the constraints at the w = -1 level. and project down onto the \Omega_k axis.

quick and dirty yes:smile: but it gives rough idea.

just graphically, from the figure, pegging at w =-1 gives an interval of
[- 0.031, 0.002] for \Omega_k
which results in an \Omega_{total} interval of
[0.998, 1.031]

I won't ascribe a sigma level to that, just say it is the projection of their dark (most favored) constraint bubble. the qualitative drift is the same.
===================

I think the deviations [from flatness] are expected at the next decimal place.

That is fascinating! Please expand a little. Quite a bit of my time at PF through 2003 and 2004 was spent defending the infinite, perfectly flat universe from people who would come in and claim it was impossible---that an infinite universe could not have resulted from a big bang. And I would say we dont know for sure that it is infinite but the bang COULD have been infinite in spatial extent and the simplest realistic looking model is infinite flat-----and so on.

I've always been a supporter of the mainstream consensus picture at least as the most likely to be right.

Now I find, to my considerable amusement, that mainstream data really is leaning towards an Omega just a wee bit larger than one!
Should we perhaps not SAY this yet:smile: should we wait for higher-ups to indicated that it is all right to say it, before we pipe up?

ray b

Mar17-06, 05:08 PM

voice of america news on this subject

http://www.voanews.com/english/2006-03-17-voa16.cfm

SpaceTiger

Mar17-06, 05:22 PM

Pegging w= -1 is easy to do visually from figure 17. Just draw an horizontal line across the constraints at the w = -1 level. and project down onto the \Omega_k axis.

It doesn't quite work that way. You have rerun the entire fit on the data to get the new best fit and error bars. They won't be wildly different, but different enough that they might be relevant to this conversation. The parameters in WMAP are often highly degenerate.

That is fascinating! Please expand a little. Quite a bit of my time at PF through 2003 and 2004 was spent defending the infinite, perfectly flat universe from people who would come in and claim it was impossible---that an infinite universe could not have resulted from a big bang. And I would say we dont know for sure that it is infinite but the bang COULD have been infinite in spatial extent and the simplest realistic looking model is infinite flat-----and so on.

Well, I'm afraid I'm not familiar enough with the popular inflationary models to say anything quantitative. The basic idea behind inflation is that it can take a universe with arbitrary geometry and then expand it exponentially such that the observable universe appears flat, despite the geometry on the largest scales. Inflation does not continue indefinitely, however, so it won't lead to perfect flatness. We believe we have a rough idea of the duration of inflation, so we also have a rough idea of how much it flattened the universe. Of course, if the universe started as flat and infinite, then it would remain so after inflation. When I say that inflation "predicts" a deviation from flatness, I'm intrinsically assuming that the universe isn't fine-tuned to be flat.

Now I find, to my considerable amusement, that mainstream data really is leaning towards an Omega just a wee bit larger than one! Should we perhaps not SAY this yet:smile: should we wait for higher-ups to indicated that it is all right to say it, before we pipe up?

It doesn't have enough statistical significance to be worth mentioning, both in my opinion and the opinion of the experimenters. It's consistent with a closed, open, or flat universe, but only at about the 1% level (using standard cosmology). I really think that's the best way to put it at this point, and that statement is based on both experience with astronomical results and the interpretations of my superiors. If the deviation becomes 2 or 3 sigma, then people will probably start to take notice. I think that's possible in the next release, though the law of diminishing returns will render the next year or two of WMAP data insigificant compared to the first two releases.

cscott

Mar17-06, 11:23 PM

Is this it? http://www.nasa.gov/vision/universe/starsgalaxies/wmap_pol.html

Chronos

Mar18-06, 02:00 AM

I seriously doubt the universe started flat and infinite. I think it has always been close to flat [at least after the first trillionth or so second] and tends toward zero over time.

marcus

Mar18-06, 11:06 AM

OK, thanks for the help. And thanks in advance for help with this!
We are talking about Spergel et al
http://lambda.gsfc.nasa.gov/product/map/current/map_bibliography.cfm
the "implications for cosmology" article that just appeared

a quick link is
http://lambda.gsfc.nasa.gov/product/map/dr2/pub_papers/threeyear/parameters/wmap_3yr_param.pdf

Please look at page 43 figure17

and you will see that the 68% confidence interval for Omega_k is

[-0.037, -0.008]

....[EDIT this is when w, the dark energy equation of state, is allowed to vary and be constrained by the data along with curvature]...

... may be moving towards a picture where we assume Omega_total is a wee bit over unity.

Dear fellow posters! I would like to specialize this thread to consider JUST the "implications for cosmology" paper that I mentioned, and any papers that come out later continuing that same particular line of investigation.

I want to focus on any controversy that arises about Omega_tot, in the wake of WMAP three-year data release. And related issues raised by the "implications for cosmology" paper.

THERE ARE HALF A DOZEN OTHER wmap PAPERS that came out, about other things.

THERE ARE MANY QUESTIONS TO EXPLORE IN OTHER THREADS, if you would care to, as well as general features of the WMAP mission and satellite to discuss.

SPACE-TIGER has initiated a general thread about WMAP and given an excellent overview. You may wish to get in on that thread for a general wide-ranging discussion.

Thanks to Ray B and to CS Scott for the links to general information and press releases. They are the best links of that sort that I have seen to date!

I hope you want to discuss and ask questions related to those links---e.g. about the significance of the polarization data etc.---in which case you might wish to raise those questions with Space Tiger in the thread he started.

Chronos, you are right on topic with what I would like to think about here. We may not be able to GET anywhere, but Omega_tot is a darned interesting issue and we ought to have it out there on the table yes?:smile:

marcus

Mar18-06, 11:48 AM

As I said in post #19, I want to focus on the Spergel et al "implications for cosmology" paper

Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology

a quick link is
http://lambda.gsfc.nasa.gov/product/map/dr2/pub_papers/threeyear/parameters/wmap_3yr_param.pdf

I see there are 23 authors:smile:

THE AUTHORS RAISE THE ISSUE OF A NON-FLAT UNIVERSE in pages 49 thru 57, in their section 7.2 entitled "Non-flat universe".

If you want to discuss on the topic of this thread, please get the PDF of that Spergel et al paper and have a look at pages 49-57.

there is not all that much to read and it's not all that hard.

BTW we should keep in mind that it is a controversial issue. the prevailing view is flat-U. But the 23 authors of Spergel et al left a crack in the door: they put in a section called "Non-flat universe" indicating that it is perhaps just barely legitimate to consider the possibility:smile:

please get the PDF, if you have any trouble let me know and i will check the link

*not here at PF, of course, where we thrive on controversy, but maybe in other venues

SpaceTiger

Mar18-06, 12:45 PM

BTW we should keep in mind that it is a controversial issue. the prevailing view is flat-U, so it would be perfectly understandable if there were a tendency to want to control or suppress* discussion of the mere possibility that the U might not be flat.

Not this again. Nobody's trying to "suppress" discussion of possibilities. In fact, it's you who's insisting on one particular possibility, I'm claiming all three options (open, closed, flat) are possible. What I'm trying to tell you is that you're overinterpreting the data. I'll be more than happy to continue discussing their error analysis, because it seems to be at the root of your misunderstanding.

But the 23 authors of Spergel et al left a crack in the door: they put in a section called "Non-flat universe" indicating that it is perhaps just barely legitimate to consider the possibility:smile:

That's right, it's two paragraphs and a bunch of figures. They conclude very simply that \Lambda CDM is consistent with the data. As scientists, we're always considering possibilities, it's our job. We don't, however, make wild claims about non-flatness without actually analyzing the data.

In the coming weeks, we may see some papers that address the issue head-on and perform a more detailed analysis of the flatness issue. If so, I think that's a great topic for discussion. These results, however, are straightforward and we won't be able to distinguish a flat from a non-flat model by staring at their figures.

marcus

Mar18-06, 01:02 PM

I'm claiming all three options (open, closed, flat) are possible...

I agree:smile:

marcus

Mar19-06, 08:11 PM

the paper I want to specialize on considering in this thread was posted today on arxiv

http://arxiv.org/abs/astro-ph/0603449
Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology

D. N. Spergel, R. Bean, O. Dore', M. R. Nolta, C. L. Bennett, G. Hinshaw, N. Jarosik, E. Komatsu, L. Page, H. V. Peiris, L. Verde, C. Barnes, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, E. L. Wright

89 pages, 28 figures, submitted to ApJ

"A simple cosmological model with only six parameters (matter density, Omega_m h^2, baryon density, Omega_b h^2, Hubble Constant, H_0, amplitude of fluctuations, sigma_8, optical depth, tau, and a slope for the scalar perturbation spectrum, n_s) fits not only the three year WMAP temperature and polarization data, but also small scale CMB data, light element abundances, large-scale structure observations, and the supernova luminosity/distance relationship. Using WMAP data only, the best fit values for cosmological parameters for the power-law flat LCDM model are (Omega_m h^2, Omega_b h^2, h, n_s, tau, sigma_8) = (0.127+0.007-0.013, 0.0223+0.0007-0.0009, 0.73 +- 0.03, 0.951+0.015-0.019, 0.09 +- 0.03, 0.74+0.05-0.06). The three year data dramatically shrink the allowed volume in this six-dimensional parameter space. Assuming that the primordial fluctuations are adiabatic with a power law spectrum, the WMAP data_alone_ require dark matter, and a spectral index that is significantly less than the Harrison-Zel'dovich-Peebles scale-invariant spectrum (n_s=1,r=0). Models that suppress large-scale power through a running spectral index or a large-scale cut-off in the power spectrum are a slightly better fit to the WMAP and small scale CMB data than the power-law LCDM model (Delta chi^2 = 3) The combination of WMAP and other astronomical data yields significant constraints on the geometry of the universe, the equation of state of the dark energy, the gravitational wave energy density, and neutrino properties. Consistent with the predictions of simple inflationary theories, we detect no significant deviations from Gaussianity in the CMB maps."

It is substantially the same as what i linked to earlier when it was at the NASA website.

a handful of other paper covering other facets of the data were posted at the same time, and will doubtless be discussed elsewhere

a particular focus of interest for me, in this "implications for cosmology" paper, is page 54
figure 17.

in this figure w (dark energy equation of state) and Omegak are both allowed to vary and both constrained by the data. When both are constrained to 68 percent confidence, a key parameter Omegatotal falls in the interval [1.008, 1.037]
My feeling is that it would be seriously over-interpreting to conclude that Omega = 1 exactly or that the universe is spatially flat. In fact one should probably keep open the possibility that the universe is not spatially flat and that Omega is slightly greater than one.

My hope is that this is not controversial and that we can wait to see how scholarly opinion develops on this issue.

marcus

Mar19-06, 09:04 PM

...
http://arxiv.org/abs/astro-ph/0603449
Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
...

I guess this arxiv preprint is pretty much the finished paper as it will appear in ApJ. Let us look at the conclusions on page 70

Here is the second of three conclusions, at the end of the paper:

"The WMAP data are consistent with a nearly flat universe in which the dark energy has an equation of state close to that of a cosmological constant, w = -1. The combination of WMAP data with measurements of the Hubble Constant, baryon oscillations, supernova data and large-scale structure observations all reinforces the evidence for dark energy."

I have highlighted "nearly flat" because it allows for the possibility that Omega is slightly larger than 1 and therefore is consistent with the idea of a spatially finite universe with a slight positive curvature.

the authors of the paper MIGHT have said flatly that
"The WMAP data are consistent with a flat universe." period.
but as it happens they did not say this---they left open another possibility to be considered.

SpaceTiger

Mar19-06, 10:01 PM

the authors of the paper MIGHT have said flatly that
"The WMAP data are consistent with a flat universe." period.
but as it happens they did not say this---they left open another possibility to be considered.

You're reading too much into their words, especially considering that on page 50, they say:

This figure confirms that our minimal model,
\Omega_k = 0 and w = −1 is consistent with the current data.

Needless to say, \Omega_k=0 is a flat universe.

Also, it should be noted that "consistent with flatness" doesn't negate other possibilities anymore than "consistent with near flatness". Consistency with one model doesn't say anything about consistency with another.

Nobody in the mainstream or on the WMAP team is trying to imply that the universe must be perfectly flat. In fact, one reason we cooked up inflation was so that we didn't have to assume perfect flatness in our models.

marcus

Mar19-06, 10:21 PM

Nobody in the mainstream or on the WMAP team is trying to imply that the universe must be perfectly flat. In fact, one reason we cooked up inflation was so that we didn't have to assume perfect flatness in our models.

Good, then there is no reason to argue is there?

You are quite welcome to imagine that I am "reading too much into their words".

As you say yourself, we don't have to assume perfect flatness!

What I am interested in emphasizing is the POSSIBILITY (among others) that the universe is spatially finite with a very small positive curvature.

No one, certainly not me, is saying this is a certainty.

this is what I said

the authors of the paper MIGHT have said flatly that
"The WMAP data are consistent with a flat universe." period.
but as it happens they did not say this---they left open another possibility to be considered.

please YOU do not read into that more than is there.

kmarinas86

Mar19-06, 10:33 PM

marcus

Mar19-06, 10:42 PM

If this is true, then this throws away the notion that a closed universe means a big crunch. So according to the latest evidence, a closed universe could be accelerating and could even lead to a big rip. There is no widely known evidence for a big crunch at this time. Did I get that wrong?

In case Space Tiger isn't handy to respond to your question. I will just offer my personal opinion that you did not get it wrong.

I'm not sure what you mean by "this" that is true. But a closed universe in the sense of Omega_total greater than 1, or spatial finiteness certainly does not by itself imply a "big crunch".

A "big rip" is the kind of thing people talk about when they are assuming a version of dark energy with the equation of state number w less than -1.

If dark energy is simply einstein's cosmological constant then w = -1 exactly----no big rip.

That's just my personal opinion. the local experts will no doubt correct me if I am wrong.

BTW hi kmarinas, glad to have company.

kmarinas86

Mar19-06, 10:48 PM

I'm not sure what you mean by "this" that is true.

"this" refers to the new WMAP data, which suggests a possibility of a closed universe.

marcus

Mar20-06, 12:25 AM

"this" refers to the new WMAP data, which suggests a possibility of a closed universe.

well it certainly suggests the possibility!

but they say their data is "consistent" with several interpretations that they mention

this is usual with academic writing, so there is not one simple message that you can say if this is true then so and so.

but I certainly agree with the general idea of what you say.
============================
BTW kmarinas, there is some good reference material on these matters
look at post #2 of the Astronomy Reference sticky thread

http://www.physicsforums.com/showthread.php?p=136400#post136400

A very good article that you see a link to there is

Charles Lineweaver
Inflation and the Cosmic Microwave Background

I posted that a couple of years ago because I found that article really really useful.

It addresses some of the issues you raised. (how accelerating expansion changes the picture from what was commonly thought pre-1998)

It also addresses something Space Tiger mentioned. One of the reasons that inflation was invented----or that people found the idea so attractive once it had been invented----is that it solved the "flatness problem".

Lineweaver talks about that IIRC. You might want to check it out. It is very readable.

there is a lot to learn in connection with this bunch of ideas (the possible spatial non-flatness of the universe----how inflation can have stretched a curved space out to be so very nearly (but not perfectly) flat. and so on.

Chronos

Mar20-06, 12:47 AM

The more important result, IMO, is 'mainstream' cosmology appears to have survived intact [and am tempted to say 'I told you so' to a few souls]. I'm intrigued that the WMAP team included Y3 results. I think it's also safe to say a huge storm of controversy is brewing. There is an incredible amount of data presented in this release and it will take years to sort out the implications. One thing that impresses me is the WMAP team went to great lengths to detail the assumptions used. I predict that will prove to be an invaluable resource for future researchers. All in all, I would say they have done a splendid job.

SpaceTiger

Mar20-06, 02:26 AM

Good, then there is no reason to argue is there?

...

What I am interested in emphasizing is the POSSIBILITY (among others) that the universe is spatially finite with a very small positive curvature.

If that's all you're interested in, then I have no argument. In fact, I'll go one further -- any measurement of the curvature of the universe that is consistent with flatness is also consistent with a small positive or negative curvature. This follows trivially from the fact that no measurement has infinitely small error bars.

When I said you were reading too much into their words, I meant that they did not choose those words to imply anything special, they were just stating the results as they were. What confuses me is why you think this is such an interesting topic of discussion as concerns the WMAP data. It has always been possible that the universe is barely closed or barely open -- WMAP has changed nothing in that arena. Also, your concerns about a finite or infinite universe will not be resolved by the measurement of the curvature because the universe can have a non-trivial topological structure (which locally appears to be open, closed, or flat).

marcus

Mar20-06, 10:31 AM

If that's all you're interested in, then I have no argument. In fact, I'll go one further -- any measurement of the curvature of the universe that is consistent with flatness is also consistent with a small positive or negative curvature. This follows trivially from the fact that no measurement has infinitely small error bars.

When I said you were reading too much into their words, I meant that they did not choose those words to imply anything special, they were just stating the results as they were. What confuses me is why you think this is such an interesting topic of discussion as concerns the WMAP data. It has always been possible that the universe is barely closed or barely open -- WMAP has changed nothing in that arena. Also, your concerns about a finite or infinite universe will not be resolved by the measurement of the curvature because the universe can have a non-trivial topological structure (which locally appears to be open, closed, or flat).

We seem to be closer to agreement now:smile:
I am glad. I do not like to argue nor am I good at it. I am not "reading in" to what Spergel et al say. I just quote them and point out what they actually said. I don't pretend to be able to get inside their heads and tell WHY they said this or that. Objectively they left open a possible interpretation. And as I think you now realize, I am not "over-interpreting the data". I quote Spergel et al's interpretation----as in figure 17 on page 50 of the arXiv preprint.

I am interested in the possibility that the universe is finite. I want to consider that possibility. You seem ready to allow me to do that in a friendly spirit. You say:
If that's all you're interested in, then I have no argument.

Again I must say I am very glad for this.

BTW You express incomprehension that I should be interested in considering this possibility (a finite universe with slight positive curvature) and gauging the consistency of that with WMAP results. That is OK, we don't have to understand each others motives.

It gets boring having to JUSTIFY being interested in something.

I may be the only one here at PF at the moment who is interested in the fact that a finite universe is consistent with the WMAP results (as one possibility) and who wants to think about that. If that is so, that's OK too. Let me get on with it. Maybe some other people will get interested later.

marcus

Mar20-06, 10:58 AM

To pick up where we left off, here is what I was saying in post #31.
Please anybody who wants to discuss these things, download the most recent version. The one posted yesterday on arXiv

...
http://arxiv.org/abs/astro-ph/0603449
Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
...

This version is the one for publication in ApJ and is slightly different from the one at the NASA site that I gave a link to a few days ago.
The main reason to all use the same version is the pagination. The key figure 17 in the "non-flat" section of the paper is on page 50 in the arXiv version, and on page 43 in the earlier version---for example.

I guess this arxiv preprint is pretty much the finished paper as it will appear in ApJ. Let us look at the conclusions on page 70

Here is the second of three conclusions, at the end of the paper:

"The WMAP data are consistent with a nearly flat universe in which the dark energy has an equation of state close to that of a cosmological constant, w = -1. The combination of WMAP data with measurements of the Hubble Constant, baryon oscillations, supernova data and large-scale structure observations all reinforces the evidence for dark energy."

I have highlighted "nearly flat" because it allows for the possibility that Omega is slightly larger than 1 and therefore is consistent with the idea of a spatially finite universe with a slight positive curvature.

the authors of the paper MIGHT have said flatly that
"The WMAP data are consistent with a flat universe." period.
but as it happens they did not say this---they left open another possibility to be considered.

I stress that I am not guessing about what they did or did not have in mind. Objectively this is what they said. Academics are usually rather careful in their wording especially in the final paragraphs of the "conclusions" at the end of a major paper. I know nothing about their intent, but intentionally or not they left open a certain possibility which I want to consider carefully.

the first question I want to think about is WHAT SORT OF OBSERVATIONAL EVIDENCE MIGHT in future SUPPORT THE NON-FLAT UNIVERSE model and might help to RESOLVE THE FINITENESS ISSUE.

As a rule in science questions are never 100 percent resolved. there are always error bars. If you get 68% someone can always ask for 95% and if you get 95% someone can ask for 98%. But people do have a sense of what is reasonable and the consensus on issues can gradually shift.

marcus

Mar20-06, 12:10 PM

...the first question I want to think about is WHAT SORT OF OBSERVATIONAL EVIDENCE MIGHT in future SUPPORT THE NON-FLAT UNIVERSE...

I am going to take my time answer this. Maybe say some more later today. But first here is something very obvious.
If you are looking for evidence for non-flat, then you want to see error bars for Omega that DO NOT INCLUDE ONE.

The first year WMAP results, if I remember correctly, had the confidence interval 1.02 +/- 0.02
or in other words [1.00, 1.04]. That was not very satisfactory.

It was inconclusive for a couple of reasons. for one thing, the flat case, Omega = 1, is still just barely in this interval. The flat case is not excluded from the interval. Also there is only a couple of digits accuracy, which is not very much.

In the three-year WMAP results there are several implied confidence intervals for Omega (I mean of course total Omega, Omega_tot, if I want to write one of the components I will use a subscript).

Several intervals are given depending on whether it is WMAP data alone, or combined with other batches of data (like Sloan Digital Sky Survey SDSS, or the supernova data). And depending on what things are being allowed to vary so we can see how they are constrained by data.

An illustrative example, from the paper we are considering, is the figure 17 on page 50 that I mentioned.

this is with COMBINED data (WMAP, SDSS, supernova, 2dFGRS) and it is where you let both w and Omega vary, since neither are known and they influence each other, and try to estimate ("constrain") both numbers SIMULTANEOUSLY.

In my view it is an impressive achievement that the Y3 data is so good that it allows one to simultaneously constrain both these things. That is why figure 17 is one of the most impressive results in the whole paper, in my opinion. In the past one would have felt obliged to PEG a value for w in order to estimate Omega----the data wasnt good enough to constrain both very effectively so you had to make an assumption about one in order to estimate the other.

Anyway the upshot is when you do all that you get, in that figure 17 case, a 68 percent confidence interval for Omega that is

[1.008, 1.037]

Notice that the FLAT CASE IS EXCLUDED FROM THIS INTERVAL. Something new. Now very obviously that is not the end of the story:smile:
That is just the beginning. 68% is not 95%, for one thing. There are more CMB missions planned.

But it illustrates how things might look some time in future and one could ask WOULD THIS TEND TO SHIFT THE mainstream CONSENSUS?

We are talking about how some of the issues might be resolved. Suppose in future some CMB mission publishes a 95% confidence interval [1.008, 1.037] for Omega.

For sake of illustration, the same interval just that it is 95% instead of 68%. Suppose.

The point is that the exact flat case of Omega = 1 exactly IS NOT IN THIS INTERVAL.

What I am talking about is an ASYMMETRY in the logic. You can never exclude the finite non-flat case if you keep getting narrower intervals but they are all around 1. Even if you narrow it down to [0.999, 1.001]
there is still the possibility that it is 1.0001 and positive curved and finite.

In case the true Omega is exactly 1, the data will always be consistent with slightly non-flat finite. Even if the interval is [0.9999, 1.0001]

But if true Omega is, say, 1.01, then you CAN hope to exclude the exactly 1 perfectly flat case. In fact an interval like [1.008, 1.037] would support that conclusion, if it were very high confidence.
Nothing in science is ever 100% certain but such a result would be very supportive and would undoubtably influence the mainstream consensus.

Of course we dont yet have a high confidence interval, we only have the 68 percent that you see in figure 17, and things like that.

There are also OTHER OBJECTIONS which I want to discuss later. Like suppose the universe really is perfectly flat if you go out way beyond the observable portion of it :smile:
this is the kind of thing people speculate about---it shades off into eternal inflation and multiverses and landscape and with some people it may shade off into a kind of fantasy world.:biggrin:

But let's not go that far. Let's just imagine that the really large scale universe is Omega =1 but the part we can see turns out to be very slightly positive curved. OK that picture would allow people who are attached to the infinite universe idea to keep their infinitude while accepting Omega > 1.

Lot of things to think about here. Plenty of possibilities to consider.

what I am expecting is that there will be a barely perceptible shift in nuance in how mainstream cosmologists talk, as they assimilate the Y3 data. I have always taken my cues from mainstream consensus people---like Charles Lineweaver and Michael Turner---over the past several years. So I want to keep alert to gradual shifts in how they (and people like them) look at things.

Occam's razor is likely going to play a role, at least for some people. If it turns out that Omega is slightly greater than one with HIGH confidence (which we dont know yet) then one SIMPLE way to interpret that is that the universe IS ACTUALLY THE WAY IT LOOKS and does have a slight positive curvature.
And then that will take some explaining, for sure! So my personal opinion is the story here is just getting started and nobody can say how the issues will resolve.

Chronos

Mar21-06, 03:00 AM

marcus

Mar21-06, 11:40 AM

I'm sympathetic, but reluctant to commit just yet marcus. A more significant issue in my mind is the value derived for w. The departure from the dark energy equation of state [w = -1] is more troublesome to me than Omega-m in making the flatness case.

Hi Chronos, I can understand. Actually there is no reason we always have to focus on figure 17. That is merely one possible way to analyze the data---one take on it. Pegging w = -1, which we would both be more comfortable with (!), seems to give qualitatively much the same result about Omega.

but if we do focus on figure 17, what you see is a 68 % confidence interval for w which is CONSISTENT with assuming w = -1 exactly. That is the interval is -1.062 (+ 0.128 or -0.079) that is

[-1.141, -0.934]

and -1 is IN that range. So that is just what one would expect to see in the case that w= -1 exactly. Which is the nice case where dark energy is just the cosmological constant that Einstein put in his equation. A comfortable old familiar mystery, not some scary new quintessence threatening to do a big rip on us.:smile:

One thing that makes me so happy with Y3 is that the data are good enough to constrain both these things at once. As I said earlier that is an impressive sign of high quality data---at least it impresses me. And AFAIK it is new. I didnt see that earlier before Y3. One of the little perks of being around at this stage in the game.

wolram

Mar21-06, 01:03 PM

I am sorry Marcus, but i have to ask how these numbers influence the
(big picture), it may be that they stand the test of time, but then the picture could change, future observations may refine them in some way up or down, and this is only one in many (derived) figures, i only say (derived) as
i have no knowledge of any fixed constants, it seems to my small brain that the juggling of many inputs can still give many outputs, i do dearly want some (big picture) and can guess your ansewer, but where are you going ?

SpaceTiger

Mar21-06, 01:07 PM

I'm prone to agree with Chronos on this one. Looking at WMAP results alone, one might be inclined to think that there is more reason to doubt the standard model's value of the curvature, but you can see very clearly that when other experiments are included, the value is almost always pulled down toward zero. This is what one would expect from a flat universe at this precision.

Dark energy, however, has been getting conflicting results in the astronomical community and the underlying theory is extremely shaky. We don't really understand where a cosmological constant would come from. WMAP fits assume a simple constant w model, but w could easily be changing with time, perhaps asymptoting to -1 at the present epoch. If their assumptions for w are wrong, then the consequences wouldn't necessarily just manifest themselves in w, they could also appear in the best-fit values of the other parameters, including the curvature.

Quite frankly, I think the vanilla cosmological constant model is going to turn out to be wrong.

marcus

Mar21-06, 02:29 PM

I am sorry Marcus, but i have to ask how these numbers influence the
(big picture), ...where are you going ?

One of the rules of the game is that you shouldn't speculate too far ahead.
When good scientists publish error bars, the hope is that future data will only narrow things down within those error bars, not jump out. And thankfully a lot of the time this is how it happens.

I see Nick (SpaceTiger) has kindly joined in the discussion. I will withhold comment in case he wants to respond to your question.

Notice that Chronos has said that he thinks it is more interesting (or "troublesome") that w is being estimated at something less than -1 (plus or minus). That is, dark energy might not simply be the Einstein equation's cosm. const. And Nick appears to agree that this is an interesting possbiliity.

I can't give you a satisfactory answer Wolram. Keep listening. maybe someone will hazard a guess.

wolram

Mar21-06, 02:50 PM

SpaceTiger

Mar21-06, 03:02 PM

I am sorry Marcus, but i have to ask how these numbers influence the (big picture)

With this analysis alone, the big result is the continuing consistency of the standard model, including evidence for inflation. These results don't say anything interesting about the possibility of a non-flat universe or a non-cosmological constant, but the data will continue to be analyzed and who knows, maybe something else will turn up.

The measurement of the slope of the spectrum of perturbations (ns) is consistent with the prediction for inflation, but the real smoking gun would be a detection of B mode polarization from gravitational waves at the surface of last scattering. WMAP doesn't have the precision to make this measurement and it's likely that we'll have to wait as much as 10 or 20 years before we see an experiment capable of reaching the level where we expect to see it.

Since WMAP is primarily probing an era when the dark energy density was small relative to matter and radiation (z~1100), it doesn't tell us very much about w. When combined with other data sets, we can improve the error bars, but much of the community would like to see an experiment dedicated to measuring w and its time derivatives. It's yet to be seen whether or not this will be realized, but there are still measurements we can do from the ground (including gravitational lensing measurements) that will improve the constraint.

The measurement of the optical depth to the surface of last scattering tells us about when the universe was reionized, which in turn tells us about when the first stars were formed. The first release had a very sketchy analysis (and subsequent) measurement of the optical depth that indicated starbirth at z~17. Improved analysis of the polarization data has brought this down to z~11. Although this gives us less time to form high-z objects (like supermassive black holes and massive galaxies), it's more consistent with the measurements of reionization from SDSS quasars, which indicate a non-negligible neutral fraction at z~6.

The WMAP data, taken alone, are leaning in the direction of a slightly closed universe, but this should be taken with a grain of salt, since other measurements tend to pull things in the other direction. I disagree with marcus that there is something interesting to be taken from that, but I certainly won't rule out the possibility that the universe is closed at this level. We shouldn't take the confidence intervals too literally, since the analysis is complex, the parameters are highly degenerate, and the systematics are not fully understood. I don't think the WMAP team would tell you that they're 68% confident the values lie within their one-sigma error bars, especially given that they often quote multiple figures (which depend on the model assumptions).

I may be forgetting something, but that's a brief review of the main results for the big picture of cosmology. Is there anything in particular you're interested in?

SpaceTiger

Mar21-06, 03:12 PM

Thank you Marcus, i wish we could consentrate on this one (enigma) do it to
death, sorry ST, Chronos, but in my mind it will not go away, is the obervational evidence a good clue? is the maths leading to a solution?

What maths are you talking about? The observational evidence, taken in full, does not put flatness outside the one-sigma error bars and we certainly aren't 68% confident that the universe is closed. I can assure you that the astronomical community doesn't consider the curvature measurement an "enigma". As for the future, high-precision measurements of the curvature might turn out to be interesting, but w is likely going to be the focus in the next 10 or 20 years.

wolram

Mar21-06, 04:03 PM

What maths are you talking about? The observational evidence, taken in full, does not put flatness outside the one-sigma error bars and we certainly aren't 68% confident that the universe is closed. I can assure you that the astronomical community doesn't consider the curvature measurement an "enigma". As for the future, high-precision measurements of the curvature might turn out to be interesting, but w is likely going to be the focus in the next 10 or 20 years.

I am very sorry i some what hi jacked Marcus,s thread, i wil bow out and
leave the question, to ,you whow know better

SpaceTiger

Mar21-06, 04:52 PM

I am very sorry i some what hi jacked Marcus,s thread, i wil bow out and
leave the question, to ,you whow know better

Nonsense, you're more than welcome to contribute, I just want to make it clear that the flatness issue is not being emphasized by the community at the moment and most (to my knowledge) don't view the measurements of flatness as being inconsistent with standard theory.

I'm just reporting the mainstream view here -- that's not necessarily the "correct" view, but it's probably the most reliable. Everyone is free to their opinion and debate is welcome on PF, I just don't want to give people the wrong impression about what the members of the WMAP team are saying. I know we're all eager to pull something exciting and revolutionary from these data, but I think it's wise to exercise some restraint, especially if our ideas run contrary to the views of the experts.

As marcus has already said, there will be a lot of discussion on this in the coming months and years, so the mainstream view may shift. I doubt, however, that it will shift very much. Spergel, Page, and company are highly respected and, as with the first release, I expect that the majority of their conclusions will be taken as the most reliable until more data become available.

marcus

Mar21-06, 05:15 PM

I am very sorry i some what hi jacked Marcus,s thread, i wil bow out and
leave the question, to ,you whow know better

Indeed you did not hijack, Wolram!

You elicited exactly the right sort of comment on what mainly concerns me in this thread! As you can see, Nick's opinion about the mainstream or "community" view differs slightly from mine. I see the view in mainstream cosmology as less consistent and more mutable than he does. Which is fine. Neither of us are, I believe, cosmologists and even a professional cosmologist might not be able to report with absolute certainty!

In a nutshell, the figure 17 on page 50 of the paper suggests the possibility that the U may be closed (i.e. spatial finite, pos. curved). However this is not the only figure or table in the paper, and there are several ways to analyze the data. It would be a good idea to actually compare some of the other things like table 11. I looked at table 11 several days ago and did NOT find it in stark contrast with figure 17.
the results always vary a little depending on what data sets are combined with WMAP and on the actual analysis performed. We could look at that again.

In any case the academic tradition is that NO one person speaks for the "official" consensus or for the community. We each have the right to our opinion. My opinion is that a finite pos curve universe is a serious possibility----something I want to discuss and understand better.

Indeed what I wish to emphasize and study very carefully in this thread is the possibility, clearly evinced by the WMAP data and by this "implications" paper, that the U is closed. I think Nick put it very nicely.

Essentially "closed" means that the true value of Omega is, with some nonzero probability (like 68 percent), inside some errorbar range which is bounded away from one. Like for example [1.008, 1.037].

I dont know whether I BELIEVE figure 17. But I want to understand better what the consequences are if something like that turns out to be correct. I don't want to simply dismiss it out of hand because it is novel or unfamiliar.

In the past it has often been assumed that Omega = 1 or that whenever we measured it we would always get some errorbar for it that was around 1------like for example [0.995, 1.005]----so then we could not rule out the case where it exactly equals one, nor could we rule out other cases, like it is a tiny bit positive.

People are accustomed to that situation, where the data is consistent both with infinite and finite cases, with flat and with non-flat. Officially that is still the situation but I sense a possible change in the wind.

SpaceTiger

Mar21-06, 06:54 PM

I've tried to avoid arguing with you directly because I know it makes you uncomfortable, but the majority of your last post was effectively in response to me, so I think it's called for now.

Neither of us are, I believe, cosmologists and even a professional cosmologist might not be able to report with absolute certainty!

Do you not count cosmology graduate students as cosmologists? Forgive me. Perhaps you would prefer the word of David Spergel, Paul Steinhardt, or Lyman Page, each of whom actually presented these results to us on the day of the release and each of whom played a part in training me. They gave no indication that the data should be taken as implying a non-flat universe (again, at this precision).

I looked at table 11 several days ago and did NOT find it in stark contrast with figure 17.

Considering that all but one of the other data sets brings the curvature estimate down so that flatness is within the one-sigma confidence interval, I'm curious to know what your definition of "stark contrast" is.

In any case the academic tradition is that NO one person speaks for the "official" consensus or for the community.

Perhaps you would prefer the term "majority view" rather than "mainstream", though I think they're both suggestive of the same thing. I don't recall using the word "official". The only sense in which my position is "official" is that it's the position of the WMAP parameters paper. I don't know how others will interpret it, but unless there arise new methods of analysis that point more strongly to a closed universe, there's no reason to think that their position will be seriously questioned. I doubt the measurement will be ignored, that is, you might see some discussion of it on arxiv, but I can assure you that the majority will need more than this to favor a closed model.

But I want to understand better what the consequences are if something like that turns out to be correct.

This, I think, is a much better topic of discussion. Bickering over the WMAP error bars is not going to go anywhere productive.

I don't want to simply dismiss it out of hand because it is novel or unfamiliar.

A closed universe is far from novel or unfamiliar, even in the inflationary paradigm. In fact, it's one of the first models taught in intro cosmology classes. What gave you the impression that it was "novel"?

My opinion is that a finite pos curve universe is a serious possibility----something I want to discuss and understand better.

You keep changing the phrasing your opinion to make it sound like I'm saying something ridiculous. I've said several times that a closed universe is a serious possibility, what I object to is your assertion that they are "68% confident that the universe is not flat".

marcus

Mar21-06, 07:19 PM

Do you not count cosmology graduate students as cosmologists?
...

You decided to specialize in cosmology! Great! Last time i remember you saying anything about that, as i recall you said your room-mate was into cosmology but not you. I may be misremembering. In any case I congratulate you.

Sorry I didnt know you had picked cosmology. Just knew you were in astro at P.

Still don't think you can report more than your opinion about the mainstream or professional consensus. There is no official "party line" is there?

I respect your opinion, your take on the community view, as such. I have my own sense of it.

Have to go, be back later.

marcus

Mar21-06, 08:06 PM

Basically I like to report on mainstream cosmology. So I have a take on it. No matter whose take, it is just opinion (there is no official spokesperson) so my take on the current situation could easily be wrong! As an exercise (and reminder of fallibility) I will try to list some ways that my view might turn out to be wrong

1. I expect a nuanced shift in how cosmologists talk about the finite/infinite, flat/nonflat issue over the coming months. If that doesnt happen, then I was wrong.

I am hardly ready to call it yet, but remember that Spergel et al, in their conclusions, said the data was consistent with a "nearly flat" universe. they could easily have said flat because in a cruder sense it IS consistent with a perfectly flat case----the data does not yet exclude that. but they didn't:smile:

that might or might not be the beginning of a nuanced shift, time will tell

2. I think it will be useful to get accustomed to thinking about and discussing the non-flat case, as one of the possibilities. So I invite discussion. What, if anything, is special about a finite (as opposed to infinite) universe?
If after learning a bit about these things and talking it over, it turns out NOT to have been useful, that will show me wrong.

I have to go, busy just now, I will try to think of different ways I could be wrong and add them to the list.

Chronos

Mar22-06, 03:17 AM

. . . but w could easily be changing with time, perhaps asymptoting to -1 at the present epoch. If their assumptions for w are wrong, then the consequences wouldn't necessarily just manifest themselves in w, they could also appear in the best-fit values of the other parameters, including the curvature.

Quite frankly, I think the vanilla cosmological constant model is going to turn out to be wrong.I think w has changed over time, which seasons, but does not entirely discredit the vanilla model. Accelerated expansion in the recent epoch suggests this, as well as [albeit to a lesser extent] inflation in the early universe.

The most gratifying result of Y3 [to me] is nailing down the third peak in the power spectrum. This, I believe, really solidifies the concordance model. When you combine it with other recent, monumental studies, like SDSS, it looks bullet-proof. We live in exciting times. While not yet fully appreciated [again IMO], WMAP is the modern day equivalent of GR.

Garth

Mar22-06, 03:49 AM

The most gratifying result of Y3 [to me] is nailing down the third peak in the power spectrum. This, I believe, really solidifies the concordance model. When you combine it with other recent, monumental studies, like SDSS, it looks bullet-proof. We live in exciting times. While not yet fully appreciated [again IMO], WMAP is the modern day equivalent of GR.
But it wasn't WMAP3 that 'nailed down' the third peak, as you can see here (http://cosmologist.info/notes/Moriond2006.ppt) (You have to press <Page Down> once, or click on the first page), a series of lecture slides by Antony Lewis of the IoA, Cambridge, England. That second slide shows the power spectrum and the WMAP3 data with Acbor, Boomerang, CBI & VSA readings superimposed.

Whereas those other experiments do trace the predicted third and even fourth peaks and beyond fairly well, the WMAP3 data does not. In particular the errors bars at l= ~870 and beyond do not even reach the predicted curve. At the third peak and beyond the other experiments are used to 'nail down' the comparison of observation with prediction.

Note in the discussion about flatness that there is a 'prior' that is so taken for granted that it is not even acknowledged: the analysis assumes GR and therefore a Friedmann model. Consequently the appearance of flatness requires \Omega_t = 1 and GR BBN requires \Omega_b = 0.02 - 0.04.

However, the first peak is consistent also with conformal flatness that may be delivered by a modification of GR. Best keep the options open...

Garth

SpaceTiger

Mar22-06, 01:20 PM

You decided to specialize in cosmology! Great! Last time i remember you saying anything about that, as i recall you said your room-mate was into cosmology but not you. I may be misremembering. In any case I congratulate you.

I haven't graduated yet, so there's no reason for congratulations, but I have been working on a thesis in cosmology for the last two years. I may have reported working on other things because we're required to do "semester projects" in a variety of areas. My roommate, quite the contrary, is working with planets and didn't even attend the WMAP talk. Some people, you know. :biggrin:

Still don't think you can report more than your opinion about the mainstream or professional consensus. There is no official "party line" is there?

If you object to the use of the word "mainstream" as sounding too general, then I'll say again, majority view. I can report the majority sentiment in this department and with less certainty the majority sentiment outside of it.

I'm not implying that anyone who suggests a non-flat universe is a crank, if that's what you're concerned about. It will be good to see if inflation can produce non-flatness at this level, just in case the high value of curvature holds. I'm pretty sure it requires fine-tuning, however, so given the confirmed predictions of inflation in other areas, I think people will need more before they start favoring a closed universe.

SpaceTiger

Mar22-06, 01:32 PM

1. I expect a nuanced shift in how cosmologists talk about the finite/infinite, flat/nonflat issue over the coming months. If that doesnt happen, then I was wrong.

Could you be more specific? I'm not even sure what that means. I would not be surprised to see papers addressing the issue (there were some of those even after the first release), but that doesn't mean the majority has shifted to believing in a positively curved universe.

I am hardly ready to call it yet, but remember that Spergel et al, in their conclusions, said the data was consistent with a "nearly flat" universe. they could easily have said flat because in a cruder sense it IS consistent with a perfectly flat case----the data does not yet exclude that. but they didn't:smile:

Actually, as I already pointed out, they did, at the end of the section on non-flatness. Again, this implies to me that you're reading too much into their words.

2. I think it will be useful to get accustomed to thinking about and discussing the non-flat case, as one of the possibilities. So I invite discussion. What, if anything, is special about a finite (as opposed to infinite) universe?

This is more of a philosophical question than a scientific one. Physicists and astronomers have traditionally tried to avoid invoking infinities in their calculations, so I think there is a natural preference towards a finite universe.

Theoretically, we expect curvature to manifest itself at levels consistent with the inflationary scenario. If they became apparent at the current precision of WMAP, it would require either a fine-tuning of inflation or an alternative theory.

SpaceTiger

Mar22-06, 01:36 PM

Note in the discussion about flatness that there is a 'prior' that is so taken for granted that it is not even acknowledged: the analysis assumes GR and therefore a Friedmann model. Consequently the appearance of flatness requires \Omega_t = 1 and GR BBN requires \Omega_b = 0.02 - 0.04.

Yes, though it should be noted that others have done an analysis of the CMB using relativistic MOND instead of GR. The problem of the third peak persists, mainly because you need an entirely separate forcing term between baryons to produce it.

marcus

Mar22-06, 01:48 PM

...It will be good to see if inflation can produce non-flatness at this level, just in case the high value of curvature holds...more before they start favoring a closed universe.

Could you please spell out what you mean in more detail. what inflation model(s)?
My memory from Lineweaver's paper a couple of years back (Inflation and the CMB) and subsequent things I've seen is that inflation FLATTENS OUT an already curved situation

Guth orig (1981 IIRC) paper was about inflation as a solution to the "horizon problem" and the "flatness problem".

you speak of inflation PRODUCING some degree or level of non-flatness.

Naive question: please clear up the apparent contradiction

majority cosmologists do not YET at this time favor closed (I agree BTW which is why I find the matter so interesting, I sense possibility for a shift in majority opinion) OK, so they dont favor closed.

Now they do like to think about a situation that started out curved, non-flat, and that inflation FLATTENED OUT.

So isnt the initial picture of something that is NOT CLOSED, not spatially finite, and nevertheless curvy? Please clarify what the common initial picture is. Is the initial U spatially infinite but just has some random bumps? Is it these random bumps that inflation flattens out?

Basically, I'd like you to say more about your words
"if inflation can produce non-flatness at this level, "

is the context for that "if" a spatially finite U, or not?

====================
[EDIT, I JUST SAW THIS]
"Theoretically, we expect curvature to manifest itself at levels consistent with the inflationary scenario. If they became apparent at the current precision of WMAP, it would require either a fine-tuning of inflation or an alternative theory."

That is interesting. What is an arxiv paper that discusses this and calculates what level of curvature IS consistent with some favored infl. scenario?

Is the estimate robust, i.e. does it depend simply on some estimate of the number of e-foldings?

SpaceTiger

Mar22-06, 03:12 PM

Could you please spell out what you mean in more detail. what inflation model(s)?
My memory from Lineweaver's paper a couple of years back (Inflation and the CMB) and subsequent things I've seen is that inflation FLATTENS OUT an already curved situation

You're correct, perhaps I should have chosen my words more carefully. The question is whether or not one can produce an inflationary model that doesn't flatten the universe beyond the limits this experiment can detect. We have constraints on the duration of inflation, as I said earlier, and thus the amount of "flattening".

So isnt the initial picture of something that is NOT CLOSED, not spatially finite, and nevertheless curvy?

The initial picture is unknown. The point is that inflation produces a nearly flat universe, regardless of initial conditions.

That is interesting. What is an arxiv paper that discusses this and calculates what level of curvature IS consistent with some favored infl. scenario?

Is the estimate robust, i.e. does it depend simply on some estimate of the number of e-foldings?

Here's a nice paper on the issue:

Knox 2006 (http://arxiv.org/abs/astro-ph/0503405)

We expect non-flatness to be detectable at the level of:

\Omega_kh^2\sim 10^{-5}

marcus

Mar22-06, 03:52 PM

Here's a nice paper on the issue:

Knox 2006 (http://arxiv.org/abs/astro-ph/0503405)

We expect non-flatness to be detectable at the level of:

\Omega_kh^2\sim 10^{-5}

Thanks! I love getting arxiv references, some I can follow or follow parts of, some i cant. but it all helps one way or another.

that 10^-5 seems way far away
because IIRC h is .73 or order 1 and therefore if I am not mistaken that is saying that Omega_k is order 10^-5

but now we are only seeing stuff order 0.01 and 0.001, too bad

not time to look at Knox right now but will get to it soon.

Nereid

Mar26-06, 08:09 PM

marcus

Mar26-06, 08:22 PM

A general question (or three) about this thread - has the main WMAP3 thread superceded the need for this, separate, thread (so we can close it, and continue discussions in the main one)? If not, what should the title of this thread be changed to (it's present title is rather inappropriate, n'est pas)?

I am interested in focusing in this thread on the issue of Omega possibly being greater than 1, and the spatial slices of the universe being closed----finite.

I would like very much to keep this thread open so that I can discuss whatever new stuff comes in on that.

There are a lot of other interesting issues regarding the WMAP3 data, so I want a thread focused on this one issue so it does not get drowned out by wideranging discussion of other stuff.

It would be rather a lot of work for me to start a new thread on the focus issue, so I would much prefer to keep this one open for that reason too.

If you have some ideas for renaming, I would like to hear them! Maybe you could send me a PM

marcus

Mar26-06, 09:49 PM

A noted cosmologist George Ellis (coauthor with Stephen Hawking of The Largescale Structure of Spacetime has been invited to contribute a chapter on Cosmology Issues to a new Elsevier Handbook
and has posted a 60 page essay, in which he devotes some attention to the finiteness or spatial closure issue

See pages 18 and 25 of this
http://arxiv.org/abs/astro-ph/0602280
Issues in the Philosophy of Cosmology
George F. R. Ellis
To appear in the Handbook in Philosophy of Physics, Ed J Butterfield and J Earman (Elsevier, 2006)

"After a survey of the present state of cosmological theory and observations, this article discusses a series of major themes underlying the relation of philosophy to cosmology. These are: A: The uniqueness of the universe; B: The large scale of the universe in space and time; C: The unbound energies in the early universe; D: Explaining the universe -- the question of origins; E: The universe as the background for existence; F: The explicit philosophical basis; G: The Anthropic question: fine tuning for life; H: The possible existence of multiverses; I: The natures of existence. Each of these themes is explored and related to a series of Theses that set out the major issues confronting cosmology in relation to philosophy."

It is clear that the book is intended to be a standard reference work for research professionals including cosmologists. I think Ellis does a fine job clearly delineating a number of issues that cosmology may address and help resolve.

Because in this thread I wish to focus on the spatial closure issue (and a possible shift in how working cosmologists treat the issue as fresh data appears) I will quote some from relevant passage of Ellis essay.

marcus

Mar26-06, 09:57 PM

In section 2.8.1 page 18 he has this list of misconceptions. I do not suggest that anyone here at PF suffers from the listed misconceptions. I quote an exerpt because it has some interesting stuff.
====exerpt=====
...
...
Misconception 5: The space sections are necessarily infinite if k = 0 or -1. This is only true if they have their ‘natural’ simply connected topology. If their topology is more complex (e.g. a 3-torus) they can be spatially finite [49, 130]. There are many ways this can happen; indeed if k = -1 there is an infinite number of possibilities.

Misconception 6: Inflation implies spatial flatness (k = 0 if and only if Omega = 1) exactly. There is nothing in inflationary theory which determines the sign of the spatial curvature. Inflationary universes are very nearly flat at late times; this is very different from being exactly flat (a condition which requires infinite fine tuning of initial conditions; if say the two millionth digit in the value of Omega is non-zero at any time, then the universe is not spatially flat).

Inflationary theory does not have the theoretical teeth required to imply that the universe has exactly flat spatial sections; hence a key issue for cosmology is observationally determining the sign of the spatial curvature, which is potentially dynamically important in both the very early universe [80, 72] and the late universe (it determines if recollapse is possible, should the dark energy decay away).
========endquote=====

SpaceTiger

Mar28-06, 05:53 PM

Misconception 6: Inflation implies spatial flatness (k = 0 if and only if Omega = 1) exactly. There is nothing in inflationary theory which determines the sign of the spatial curvature. Inflationary universes are very nearly flat at late times; this is very different from being exactly flat (a condition which requires infinite fine tuning of initial conditions; if say the two millionth digit in the value of Omega is non-zero at any time, then the universe is not spatially flat).

That's right. As was explained in the other paper I linked, the primordial power spectrum that arises from inflation (nearly scale invariant) predicts deviations from flatness at about the 0.001% level. This doesn't say anything about the sign of the curvature, just the magnitude of the random fluctuations at that scale. Since the fluctuations are theorized to be random, we could be living in an overdensity, underdensity, or average part of the universe. However, if the universe were overdense or underdense by a very large amount (i.e. flat or non-flat at levels beyond that precision), it would be very suspicious and possibly indicate that there is a problem with the standard model.

marcus

Mar28-06, 09:18 PM

... scale invariant) predicts deviations from flatness at about the 0.001% level. This doesn't say anything about the sign of the curvature, just the magnitude of the random fluctuations at that scale. Since the fluctuations are theorized to be random, we could be living in an overdensity, underdensity, or average part of the universe. ...

Thanks for your comment.

I looked at the Knox paper and I interpret it to mean that even if the universe is not spatially closed it might have random fluctuations in curvature local to our observable part of it that are on the order of 10^-5 in Omega

that is + or - 0.00001

so we are talking about a possible observation of, say, Omega = 1.00001.

I think this is in line with what you are saying, you say A THOUSANDTH OF A PERCENT which is just the 0.00001 or the 10^-5 that Knox says.

I won't be thinking of Omega = 1.00001 as a condition that would imply spatial closure.

I think you probably agree, if I understand what you say.

the topic of the thread here, and what I want to consider, is the possibility left open by WMAP3, which future measurements could confirm, of a much larger positive curvature---like Omega = 1.01----and a universe with closed spatial sections (as all know that could also occur in the flat case with special topology so substantial positive curvature is just one possible condition implying what we are talking about)

have to go, but will be back later

marcus

Mar28-06, 10:20 PM

I have some quotes from Ned Wright (the cosmologist at UCLA whose website and its cosmo. tutorial many of us have visited) and from George Ellis that I want to put in.

this will help give an idea of what some selected people are saying now and later on we can see if there has been any significant shift in the message.

Here is George Ellis on page 25 of his "Cosmology Issues" essay
====exerpt=====

4.2.3 Determining the RW parameters [Robertson-Walker]

Given that a RW geometry is a good description of the observable universe on a large scale, the further issue is what are the best-fit parameters that characterize it, selecting the specific universe we observe from the family of all FL models (Sec.2.1). Important observational issues are:

• Determining the Hubble parameter H_0, which sets the overall scale of the observed universe region.

• Determining the trio of the density parameter Omega_0, deceleration parameter q_0, and cosmological constant Lambda (or equivalently the density parameter Omega_Lambda), which are the major defining characteristics of a specific Friedman-Lemaitre model. The CBR data, supernova observations, deep number counts, source covariance functions, velocity measurements, and gravitational lensing observations can determine these quantities.

• Determining the sign of the curvature k, showing whether the universe has closed spatial sections and also whether it is possible for it to recollapse in the future or not. Analyses of the observations should always attempt to determine this sign, and not assume that k = 0 (as is often done).

• Various parameters are used to characterize the nature of dark matter (Sec.2.3.6) and dark energy (Sec.2.3.5). As their dynamics is unknown, these too have to be determined observationally.
=====endquote=====

It seems to me that Ellis is critical of some of his fellow cosmologists for favoring the SPATIALLY NON-CLOSED picture to such an extent that, according to him, they "often" TAKE IT FOR GRANTED. This is how I understand what he says here.

Interestingly enough today Ned Wright posted something on arxiv that sends a similar message. Let me get it.

marcus

Mar28-06, 10:38 PM

Conceivably someone reading this thread might be interested by what Ned Wright had to say about this in something he put on arxiv today:
http://arxiv.org/abs/astro-ph/0603750
A Century of Cosmology
E. L. Wright (UCLA Astronomy)
Talk presented at the "Relativistic Astrophysics and Cosmology - Einstein's Legacy" meeting in Munich, Nov 2005. Proceedings will be published in the Springer-Verlag "ESO Astrophysics Symposia" series. 10 pages with 2 figures

AS ONE OF HIS FIGURES Wright has a caricature of a cosmologist's CIRCULAR ARGUMENT: It is his Figure 1. A big circle of words evidently meant as a joke. It has these words going around the circle:

"If w = - 1, then flat LambdaCDM is a good fit to all the data. If Omega = 1 , then w = - 1 is a good fit to all the data."

He is opposed to assuming flat. Explaining this Figure 1. he says
"However, there is a very strong tendency among theorists to assume the Universe is flat when seeking w and w'. This is a logical error, since the evidence for a flat Universe comes from the agreement of the concordance LambdaCDM model with all the data. But the concordance LambdaCDM model has w = -1 and w' = 0 exactly. If w and w' are allowed to vary, then the evidence for a flat Universe must be re-evaluated. ... "

Unfortunately I have to go out now so can't finish this post but will get back to it later.

========
I'm back now. Yeah. I think to put it simply the message of what Wright says, and of his figure 1, is that IT IS NOT COOL ANYMORE TO ASSUME FLAT.

Wright is a leading cosmologist, in case any reader doesnt know----he was one of a group of top scientists in charge of WMAP----so you see his name as co-author on some main WMAP papers. But he was an important figure already before that.

=========

Eventually I will get over to the Astronomy building and talk to some grad students---in the coffeeroom or in one of their offices. So far I am going on signals i get from bigname people like George Ellis and Ned Wright, and from things like Figure 17 of the Spergel et al paper. But I would also like to talk with some of the "troops on the ground". Over the years I've done that on occasion and they (random grad students) have been very helpful. that should give additional perspective on a possible shift.

Chronos

Mar29-06, 02:09 AM

marcus

Mar29-06, 01:12 PM

Marcus, I agree in spirit with Ned Wright's analysis, but am reluctant to accept the conclusion. There are too many conflicting observations that cannot be ruled out. Maybe, in 100 years, the answer will become obvious. For now, I cannot accept that assertion.

You are heartily welcome to whatever your attitude is:smile: but I dont understand what you think is his "conclusion" or his "assertion" that you say you can't accept.

Wright is a working cosmologist who was involved in the planning execution of WMAP and in the analysis of WMAP3. He is talking about what to do TODAY, not in 100 years. Nothing visionary here.

He says that if you want to find out about w, then you should let BOTH w and Omega VARY SIMULTANEOUSLY and use the data to constrain both.
He says that you should not peg Omega = 1 and then calculate w

and he says you should not peg w = -1 and then calculate Omega.
He says, to put it simply, IT IS NOT COOL TO ASSUME FLAT i.e. to assume Omega = 1.

this could be seen as just good scientific advice to people doing analysis of data today and tomorrow.

He actually goes further and says that you should let w AND its timederivative w' AND Omega vary and try to constrain them all. To allow for the possibility that w could be changing. But the simple version of the message is to let Omega and w vary----which incidentally was what was done in Figure 17 of Spergel et al, the figure which I liked so much and discussed earlier in this thread. That Figure illustrates a simple version of what Wright advocates doing.

Wright makes this the message of his Figure 1 , and his conclusions paragraph, of the paper he put on arxiv yesterday.

I'm happy for you to be as reluctant as possible but I just want to make sure we are on the same page and both talking about the same conclusions of the same Ned Wright paper! As long as we understand what we're talking, then I'm delighted if you have a negative reaction. It illustrates what I think is a majority, or at least very common, attitude in the field----and one which Wright is addressing---and one which I think will gradually shift over the coming little while. We will see:smile:

marcus

Mar29-06, 01:31 PM

As could be expected, since Ned Wright is a key figure in this whole business, and one of the WMAP project leaders, he is one of the co-authors of the "Implications for Cosmology" paper which is the basis for this thread.

this is the paper we call "Spergel et al".
I should put the link again, in case someone drops into this thread and wants to look at the WMAP3 results "implications for cosmology"

http://arxiv.org/abs/astro-ph/0603449
Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology

the Figure 17 is on page 50 IIRC, in case anyone wants to check it out

SpaceTiger

Mar29-06, 01:42 PM

I attended a talk yesterday in which the speaker was discussing future methods of measuring curvature and dark energy parameters. In the next ten or twenty years, they expect to be able measure curvature to at least one more decimal place and perhaps two. The seemingly best method of doing this is with weak lensing surveys, but Type Ia supernova, cluster counting, and baryon oscillation experiments should do comparably well.

He also discussed methods of actually testing GR (which would be refreshing) by measuring dark energy parameters and then comparing the predicted and measured growth functions, which describe the growth of perturbations in a general relativistic universe.

In the middle of his talk, he flashed up your favorite graph from the WMAP3 paper, but gave no indication that he thought it was suggestive of a universe with positive curvature.

marcus

Mar29-06, 02:28 PM

I attended a talk yesterday in which the speaker was discussing future methods of measuring curvature and dark energy parameters. In the next ten or twenty years, they expect to be able measure curvature to at least one more decimal place and perhaps two...

COOL!

In the middle of his talk, he flashed up your favorite graph from the WMAP3 paper, but gave no indication that he thought it was suggestive of a universe with positive curvature.

Fine, in a certain sense that gives us a kind of benchmark for where people's heads are, at the moment. I should really go talk to some of the local grad students. that will also give a benchmark, I can then come back later and gauge if any change.

marcus

Mar29-06, 08:38 PM

I don't recommend this article---on the contrary: apologize for even mentioning it---and so wrote the mention in white

http://arxiv.org/abs/astro-ph/0603690
Cross-correlation of WMAP 3rd year and the SDSS DR4 galaxy survey: new evidence for Dark Energy
A.Cabre, E.Gaztanaga, M.Manera, P.Fosalba, F.Castander (IEEC/CSIC)
5 pages, 5 figures, submitted to MNRAS Letter
We cross-correlate the third-year WMAP data with galaxy samples extracted from the SDSS DR4 covering 13% of the sky, increasing by a factor of 3.7 the volume sampled in previous analyses. The new measurements confirm a positive cross-correlation with higher significance (total signal-to-noise of about 4.7). The correlation as a function of angular scale is well fitted by the integrated Sachs-Wolfe (ISW) effect for LCDM flat FRW models with a cosmological constant (w=-1). The combined analysis of different samples gives Omega_L=0.75-0.80 (68% Confidence Level, CL) or 0.70-0.82 (95% CL). We find that the best fit Omega_L decreases from 0.82 to 0.75 (95% CL) when we increase the median redshift of the galaxy sample from z~0.3 to z~0.5. The quick drop of the measured signal with z is too fast for the LCDM cosmology. The data can be better reconciled with a model with an effective dark energy equation of state w<-1.5. Such phantom cosmology reduces by up to ~20% the amplitude of the lower multipoles of the CMB temperature anisotropies with respect the w=-1 prediction, which also brings the models closer to the observations.

I find the idea of w<-1 repugnant, as do all rightthinking ppeople I would hope. there is a strong appeal of the two ideas w = -1 exactly and Omega = 1 exactly (or 1 with a little random quantum ripple).
However these people (Spaniards, I see) find something about the WMAP3 data suggests to them w way less than -1. Even in my favorite Spergel figure 17 the 68% confidence interval for w only goes down to -1.14 and they are below that. Yuk. Is this a sign of the times?

=========================
the main paper we are assimilating in this thread is "Spergel et al", the "implications for cosmology" paper that has Ned Wright as a co-author.
I should put the link again:

http://arxiv.org/abs/astro-ph/0603449
Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology

Have another look at Figure 17 is on page 55 IIRC, to see what it would mean to contemplate the unpalatable idea that w might be less than -1.

Chronos

Mar30-06, 01:46 AM

The best fit models proposed by Spergal et al. still suggest, without insisting that w is very close, if not exactly -1. I think that is just good science.

marcus

Mar30-06, 01:38 PM

The best fit models proposed by Spergel et al. still suggest, without insisting that w is very close, if not exactly -1.

that is right. Personally I tend to assume w=-1 exactly, which would be consistent with a positive curved, spatially closed, finite, universe if you favor that picture. And also consistent with other cases as well! Essentially it just means that the dark energy corresponds to Einst. cosmological constant. But my liking to assume w=-1 is a personal bias which I try to discount and avoid infecting my judgment. One reason I do this is because of what Ned Wright says.
http://www.physicsforums.com/showpost.php?p=949832&postcount=72
http://arxiv.org/abs/astro-ph/0603750

...that is just good science

One of my guides regarding "good science" is Ned Wright, and he says to let w and Omega (and maybe even w') vary simultaneously. that is, when you are trying to estimate w (the DE EOS) you should not make any assumption about the universe being flat or not. Although the darkenergy EOS is nominally separate from flatness or spatial closure issues, they can influence each other in the calculation, so it should be treated that way when you analyze. One should make an effort to avoid prejudice about Omega when one estimates w-----in other words let them both vary simultaneously and constrain both.

In a nutshell, he says "do not peg Omega = 1 when you estimate w, and do not peg w = -1 when you estimate Omega" because they both might not be those numbers and pegging can skew the fit.

So the kind of analysis that results from doing what he says is Figure 17 on page 55, and here is a quote from the caption:

The contours show the 2-d marginalized contours for w and Omega_k based on the the CMB+2dFGRS+SDSS+supernova data sets. This figure shows that with the full combination of data sets, there are already strong limits on w without the need to assume a flat universe prior. The marginalized best fit values for the equation of state and curvature are w = -1.062 (+0.128 -0.079) and Omega_k = -0.024 (+0.016 -0.013) at the 68% confidence level.

What that says about w is that at 68% confidence it is in the interval
[-1.141, -0.874]

That is the darkenergy EOS is in an interval AROUND -1, and estimate varies roughly on the order of TEN PERCENT around -1.

this is how i might make sense if someone says " w is very close, if not exactly -1"
I don't object if they want to say it that way. In some contexts, on some days, if I am feeling right, I also would say that roughly 10% is "very close, if not exactly":smile:

And because of my confessed bias, I am quite happy with that 68% interval around w = -1. So fine! All well and good.

But this does not say anything about SPATIAL CLOSURE, does it Chronos?

For that, if one is following Ned Wright's guidelines for good science and allowing both w and Omega to be constrained simultaneously, one gets the 68 % confidence interval for Omega which is

[1.008, 1.037]

The point is that this interval is NOT AROUND ONE.
It does not prove anything but it is CONSISTENT with some positive overall curvature and with spatial closure. So that is a possibility:smile: which it is "good science" (to use your expression) to keep in mind.

marcus

Apr16-06, 08:15 PM

To remind readers, one bit of news from WMAP3 data was that when w (DE EOS) and curvature were simult. constrained by the data you got a 68% conf. interval for Omega that NO LONGER STRADDLED ONE.

The interval for Omega referred to is [1.008, 1.037]
Discussed in Spergel et al Fig 17 page 53. So the centipede upstairs is getting ready for bed and we heard a shoe drop.

We listen for other shoes. Will the scientific community gradually change the nuances in how it talks about this. If Omega REALLY WERE like 1.01 that would be consistent with a spatial finite universe, that is with SPATIAL CLOSURE. Like a big 3-sphere instead of infinite flat euclid 3-space.

OK, this thread is for listening for shoes drop. Don't be in a hurry, just wait. here is a little bump. what does it mean, if anything?

http://arxiv.org/abs/astro-ph/0604335
Cosmological parameters from combining the Lyman-alpha forest with CMB, galaxy clustering and SN constraints
Uros Seljak, Anze Slosar, Patrick McDonald
11 pages, 4 figures

"We combine the Ly-alpha forest power spectrum (LYA) from the Sloan Digital Sky Survey (SDSS) and high resolution spectra with the cosmic microwave background (CMB) including 3-year WMAP, supernovae (SN) and galaxy clustering constraints to derive new constraints on cosmological parameters. The existing LYA power spectrum analysis is supplemented by constraints on the mean flux decrement derived using a principal component analysis for quasar continua, which improves the LYA constraints on the linear power. The joint analysis reduces the errors on all parameters and prefers the simplest 6 parameter cosmological model. We find some tension between the WMAP3 and LYA power spectrum amplitudes, at the ~2 sigma level, which is partially alleviated by the inclusion of other observations: we find sigma_8=0.85+-0.02 compared to sigma_8=0.80+-0.03 without LYA. For the slope we find n_s=0.965+-0.012. We find no evidence for running of the spectral index, dn/dln k=-0.020+-0.012, in agreement with inflation. The limits on the sum of neutrino masses are significantly improved: sum(m_nu)<0.17 eV at 95% (<0.32 eV at 99.9%). This result, when combined with atmospheric and solar neutrino mixing constraints, requires that the neutrino masses cannot be degenerate, m_3/m_1>1.3 (95%). Assuming a thermalized fourth neutrino we find m_s<0.14 eV at 95% c.l. and such neutrino cannot be an explanation for the LSND results. The fit is poor even in the limit of massless sterile neutrino since the constraint on the number of relativistic neutrino species is N_nu=3.19+0.19-0.15 and N_nu>4 is excluded at 99.76%. The constraint on the dark energy equation of state is w=-1.04+-0.06. The constraint on curvature is Omega_k=-0.003+-0.006. Cosmic strings limits are G mu<2.3 10^-7 at 95% c.l."

======================

mean anything? not much I am afraid, more a point for the status quo this time.

It puts Omega in the interval [0.997, 1.009]
which is comfortably consistent with the idea that Omega true value is EXACTLY ONE.

Chronos

Apr17-06, 04:26 AM

I was reading that same paper today, marcus, and left with the same feeling - wrapped in an old, handmade quilt. WMAP 3 seems to lean in the direction of closure [omega just barely above 1]. Not enough to be compelling, but tantalizingly close. In short, I still think omega is exactly 1.

marcus

Apr17-06, 07:59 AM

...and left with the same feeling - wrapped in an old, handmade quilt...

cant say anything about Omega at the moment, but quilts are nice arent they. my wife has taken part in several handmade quilt projects---her sister is the real quiltmaker in the family

my favorite thing to read cosmology related papers in is an unbelieveably thick cushy blue terrycloth bathrobe

the centipede upstairs has a lot of shoes left to drop

SpaceTiger

Apr17-06, 01:05 PM

mean anything? not much I am afraid, more a point for the status quo this time.

It doesn't mean much because it agrees with the standard model? We shouldn't get into the habit of de-emphasizing results simply because they produce no surprises. Remember, the Ly\alpha forest is one of the best cosmological constraints we have and, as they say in the paper,

This is the strongest constraint on the curvature to date and the data continue to show no evidence for it.

Chronos

Apr18-06, 01:37 AM

I agree with ST, marcus. Observational evidence still overwhelmingly favors the LCDM model. While anomalous observations remain to be explained [e.g., Arpianism], there are not enough to 'throw out the baby with the bath water'.

marcus

Apr30-06, 08:27 PM

...

the centipede upstairs has a lot of shoes left to drop

here's another

http://arxiv.org/abs/astro-ph/0604616
Extending the WMAP Bound on the Size of the Universe
Joey Shapiro Key, Neil J. Cornish, David N. Spergel, Glenn D. Starkman
9 pages, 16 figures

"Clues to the shape of our Universe can be found by searching the CMB for matching circles of temperature patterns. A full sky search of the CMB, mapped extremely accurately by NASA's WMAP satellite, returned no detection of such matching circles and placed a lower bound on the size of the Universe at 24 Gpc. This lower bound can be extended by optimally filtering the WMAP power spectrum. More stringent bounds can be placed on specific candidate topologies by using a a combination statistic. We use optimal filtering and the combination statistic to rule out the infamous "soccer ball universe'' model."

I still claim that the results so far don't mean very much in the sense that I plan to wait for a good deal more reaction. these links are not intended to prove anything either way. they are sampling the MWAP3 fallout.

Niel Cornish is an amusing guy. I remember 3 years or so back his paper about how the U has to be "at least this big". He had a pet monkey that appeared sitting on Cornish shoulder in a picture at his website (Cornish site, not the monkeys)

Make whatever conclusion you want. I'm just collecting some post WMAP3 papers related to the issue of Universe closure or non-closure.

==========================
for the curious, some samples from this particular dropped shoe:

"...The WMAP data point to a universe with a total energy density within 2% of critical[3]. This means that even if space is not quite flat, the radius of curvature of the Universe is at least of order the size of the observable Universe, and space can be considered to be nearly flat. ..."

can be considered, I may add, to be FINITE and nearly flat------if one cares to so consider it :wink:

I don't particularly like the models with complicated topology such as the DODECAHEDRON thing. So I am glad to see them ruling it more and more out

"XI. CONCLUSION The claim that the topology of our Universe had been found to be that of the Poincaré dodecahedron does not stand up under scrutiny. The signature found in Ref. [8] disappears when one uses the proper S statistic and considers the false positive threshold. While the shape of our Universe remains a mystery, the matching circles test can be used to place a lower bound on the size of the Universe. The previous limit of 24 Gpc [4] can be extended by about 10% using filtering of the WMAP power spectrum. A full search with optimal filtering is now underway. "

more power to you, guys. So roughly speaking the U is sure to be at least some 30 billion parsecs across. Roughly 100 billion light years.

you know that you can find two points that far apart

and hey, it might be flat-out infinite too. we still dont know:smile:
in my unauthoritative opinion.

SpaceTiger

Apr30-06, 09:06 PM

It was an interesting result after the first release, but this release just gives a 10% increase on the topology scale limit. Meh, I guess somebody had to check.

Note that this method more directly addresses the finiteness question than a measurement of the curvature. If the cosmological principle breaks down at large scales, the universe can have any curvature and still be finite. However, I think the detection of circles on the sky would definitively rule out an infinite universe.

marcus

Apr30-06, 10:40 PM

... However, I think the detection of circles on the sky definitively rules out an infinite universe.

I agree. Thanks for the comment. As you say, circles would rule out infinite, and AFAIK they have not been seen.
(my gut reaction to circles is horror. I hope they are never observed. Rather see simple vanilla infinite than some periodic structure. but decency forbids dwelling on one's prejudices)

Chronos

May1-06, 01:29 AM

I think we can safely rule out 'circles in the sky'. And I share your discomfort with that concept. But, I'm not convinced it rules out a finite, unbounded universe. My concern centers around the argument the universe very much appears to be temporally finite. Hence, I am forced to reject any argument it [the observable universe] is spacially infinite.

marcus

May18-06, 08:44 PM

BTW Ned (SpaceTiger) is coming out very well as a guesser that the community would NOT show signs of shifting off the flat assumption any time soon. If that was his guess.

My guess was different and would have been that by now i would have heard more about it. And I havent. But I expect to just have to wait longer than I at first expected, and am not discouraged.

Today, another paper

Look at Figure 2, on page 4

Shows a 68 % confidence region for Omega_matter and Omega_Lambda where sure enough the {Omega_total = 1} line DOES pass thru, but rather off to one side. So sure enough the data is CONSISTENT with the convenient usual assumption of Omega_total = 1, that is "flat".

And in their verbal treatment the "flat" case is the only one they appear to consider.

And a casual glance at Figure 2 shows that the "SWEET SPOT" of their 68% gaussian oval has about Omega_total = 1.1 roughly.

which as usual if we took it seriously would say "positive curved spatially closed" but which as usual we do not take seriously but attribute to mere vagary of the data.

the funny thing is it seems to happen all the time.

The Hubble diagram extended to z>>1: the gamma-ray properties of GRBs confirm the Lambda-CDM model
C. Firmani (1,2), V. Avila-Reese (2), G. Ghisellini (1), G. Ghirlanda (1) ((1) Osserv. Astron. di Brera, Italy; (2) Instituto de Astronomia, U.N.A.M., Mexico)
5 pages, 4 figures included. Submitted to MNRAS Letters

"Tight constraints on cosmological parameters can be obtained with standard candles spanning a range of redshifts as large as possible. We propose to treat SN Ia and long Gamma-Ray Bursts (GRBs) as a single class of candles. Taking advantage of the recent release of the Supernova Legacy Survey and {\it the recent finding of a tight correlation among the energetics and other prompt gamma-ray emission properties of GRBs}, we are able to standardize the luminosities/energetics of both classes of objects. In this way we can jointly use GRB and SNIa as cosmological probes to constrain Omega_m and Omega_L and the Dark Energy equation of state parameters through the same Bayesian method that we have, so far, applied to GRBs alone. Despite the large disparity in number (115 SNIa versus 19 GRBs) we show that the constraints on Omega_m and Omega_L are greatly improved by the inclusion of GRBs. More importantly, the result of the combined sample is in excellent agreement with the Lambda-CDM concordance cosmological model and does not require an evolving equation of state for the Dark Energy."

As you recall in the WMAP3 report there was that figure with 68% confidence interval Omega_total being
[1.008, 1.037], not even around one! This is much broader and less precise, but it is around one (just a bit off to the upside)

Garth

May19-06, 05:59 AM

BTW Ned (SpaceTiger) is coming out very well as a guesser that the community would NOT show signs of shifting off the flat assumption any time soon. Is that flat or conformally flat?Today, another paper

Look at Figure 2, on page 4

Shows a 68 % confidence region for Omega_matter and Omega_Lambda where sure enough the {Omega_total = 1} line DOES pass thru, but rather off to one side. So sure enough the data is CONSISTENT with the convenient usual assumption of Omega_total = 1, that is "flat".
(emphasis mine)

Note, it is actually the other way round - deductions from the data of standard candles and rulers, as well as CMB anisotropies, are dependent on the spatial geometry of the universe.

These data sets are indeed observed to be consistent with a spatially 'flat' geometry and it is this 'flatness' that requires \Omega_{total} = 1. However, THAT deduction leads to the invocation of problematic DE.

Conformally flat geometries are also consistent with these data sets, but they do not require \Omega_{total} = 1, and so DE may not exist after all.

Note further, the linearly expanding universe is also consistent with the distant S/N Ia data, however, such a conformally flat geometry and linearly expanding scale factor would require a modification of GR.

Garth

Chronos

May19-06, 06:19 AM

If we leave out the alleged CMB anisotro[cow]pies, the puzzle box is not that difficult to solve.

Garth

May19-06, 07:50 AM

If we leave out the alleged CMB anisotro[cow]pies, the puzzle box is not that difficult to solve.
Well, the puzzle box now includes problematic DE, exotic non-baryonic DM, Higgs bosons/inflatons, (all as yet undiscovered in laboratory physics), a possible age problem in the early universe, as well as a Pioneer anomaly, and the alleged axis of evil and deficient quadrupoles.

Agreed, those puzzles may be solvable, nevertheless, it is important to keep viable options open, we may never know what may lay round the next corner! :wink:

Garth

selfAdjoint

May19-06, 08:06 AM

Well, the puzzle box now includes problematic DE, exotic non-baryonic DM, Higgs bosons/inflatons, (all as yet undiscovered in laboratory physics), a possible age problem in the early universe, as well as a Pioneer anomaly, and the alleged axis of evil and deficient quadrupoles.

Agreed, those puzzles may be solvable, nevertheless, it is important to keep viable options open, we may never know what may lay round the next corner! :wink:

Garth

Bolded matter is a bit of a stretch for cosmology? Why not include the non-mating of quantum and GR then, or just the whole world of things unknown in all of physics?

Garth

May19-06, 08:10 AM

Bolded matter is a bit of a stretch for cosmology? Why not include the non-mating of quantum and GR then, or just the whole world of things unknown in all of physics?Indeed, why not include the QM/GR interface in the puzzle box?

Modern cosmology is founded on both.

As I said, just as well to keep all viable options open.

Garth

SpaceTiger

May20-06, 04:41 AM

BTW Ned (SpaceTiger)

My name is Nick.

...is coming out very well as a guesser that the community would NOT show signs of shifting off the flat assumption any time soon. If that was his guess.

It wasn't exactly a "guess", I work with the people doing the experiment. The issue is not one of physical interpretation, just of interpretation of quoted errors. The community has no particular reason to question the WMAP team's interpretation of their own errors. The only way you could see a change of the community's view of "flatness" is if somebody incorporated more data or the error analysis was shown to be flawed.

And a casual glance at Figure 2 shows that the "SWEET SPOT" of their 68% gaussian oval has about Omega_total = 1.1 roughly.

which as usual if we took it seriously would say "positive curved spatially closed" but which as usual we do not take seriously but attribute to mere vagary of the data.

You're talking about a data set that only constrains \Omega_k to ~20% and which includes unity in what appears to be a <50% confidence interval. By contrast, the precision of WMAP is of order a percent or two. You'd need ~100 such independent results with minimal systematics to even begin to compare to WMAP's constraint on flatness.

the funny thing is it seems to happen all the time.

Not in my experience. When WMAP was included with other data sets (such as SDSS), the vast majority of them brought the estimate on \Omega_k down.

marcus

May20-06, 10:40 AM

My name is Nick.
...
Of course Nick Bond! Just carelessness, sorry.

thanks for jogging my memory, which needs it sometimes. I just saw a list of your papers on arxiv
http://arxiv.org/find/grp_physics/1/au:+bond_N/0/1/0/all/0/1

Impressive! congratulations!

the search turned up 9 papers. I remember you saying you were in the PhD program at Princeton. You must be nearly done, finishing up thesis and so on.

Not in my experience...

You have such different experience of this from me, which makes life interesting.
My experience is that for some years now whenever I see ANY estimate of Omega_total it is NEVER on the downside of one.

whatever the dataset or the way it is measured it is always plain 1, or the confidence interval is LOPSIDED towards the upside (but still includes 1). Or else as in that WMAP3 case which we discussed, the confidence interval is ENTIRELY on the upside of 1 and doesnt even include 1.

One certainly doesnt want to over-interpret the data! (Seriously, no joke!) One wants to be very sober and judicious about this and refrain from attributing undue significance!

But my nagging experience is that the published confidence intervals always come out a bit upside, and never downside.

I assume that you, Garth, Chronos and so on HAVE seen confidence intervals that are lopsided downwards. Indeed one may INFER the existence of datasets that do make for such (like Sloan Digital Sky Survey) because MIXING SDSS data with WMAP3 data brings Omega down! I have seen a bunch of mixed data results tabulated in Spergel et al. As you indicate. But that is inference. the fact is, I have not seen anybody make a confidence interval (recently at least) that is on downside of one.

Maybe someone wants to supply a link?

It is curious that your experience is different.
=====================
I think we have already been through much of this discussion and there is no need to repeat.

But if you do happen to have a link to some recent published estimate of Omega that has a confidence interval downwards of one (in contrast to what I have seen), that would be something NEW for me and I would be very glad to see it.

Please give a page reference with the link. This is something that may have been staring at me all the time and my sometimes overworked eyes did not spot!

SpaceTiger

May20-06, 03:08 PM

Maybe someone wants to supply a link?

The 2dF measurements of large scale structure yield an estimate of curvature that is not only low, but almost two-sigma below flat at a precision of ~5%:

Cosmological parameters from CMB measurements and the final 2dFGRS power spectrum (http://lanl.arxiv.org/abs/astro-ph/0507583)

Refer to Table 2.

You have such different experience of this from me, which makes life interesting.
My experience is that for some years now whenever I see ANY estimate of Omega_total it is NEVER on the downside of one.

This should suggest to you that something's wrong. To see what I mean, let's just suppose for the moment that you're right about the curvature being positive and let's take the upper WMAP error bar -- \Omega_{tot} = 1.038. Now let's ask the question, if perform an experiment with gaussian random errors on this parameter of order 20% (as in the paper you just quoted), what fraction of the time will I measure \Omega_{tot}>1? The answer is about 57.5% of the time. That means that, even in the upper range of curvature suggested by WMAP, you should still see such measures give \Omega_{tot}<1 in 42.5% of data sets. The fact that you never see such things suggests one or more of the following:

1) Your sample is too small to be meaningful.
2) Your sample is heavily biased.
3) The measurements you're thinking of are not all independent.
4) The experiments you're thinking of suffer from systematics that always bias them greater than one.
5) The experiments have overestimated their error bars.

The last two things seem pretty unlikely to me, so you should probably consider looking into the first three.

marcus

May20-06, 03:49 PM

The 2dF measurements of large scale structure yield an estimate of curvature that is not only low, but almost two-sigma below flat at a precision of ~5%:

Cosmological parameters from CMB measurements and the final 2dFGRS power spectrum (http://lanl.arxiv.org/abs/astro-ph/0507583)

Refer to Table 2.

...
3) The measurements you're thinking of are not all independent.
...

this is an excellent one to add to the collection, thanks. It is from July 2005, so fairly recent though not the most so. Let's see what it says.
I am looking at Table 2, as you suggest. don't have time to study it at length but here's what I see it say:

the Omega_k error bar is around ?0.074 with limits +0.049 and -0.052

so as I read it the error bar is between [-0.126, -0.025]

this is reminiscent of my positive curvature benchmark Spergel et al

folks will recall Figure 17 on page 55 of the famous WMAP3 report by Spergel et al "implications for cosmology" where they gave a 68 % confidence interval for Omega_k which was
" ?0.024 +0.016 ?0.013 at the 68% confidence level."

this translates into [-0.037, -0.008]

that Spergel et al interval meant that we had Omega in the range
[1.008, 1.037]

that is the curious upside picture I see a lot of

OF COURSE THESE CONFIDENCE INTERVALS PEOPLE PUBLISH ARE NOT SEPARATE INDEPENDENT MEASUREMENTS, I am not doing statistics with them:smile: , THEY ARE ALL BASED ON THE SAME FEW DATASETS, like SDSS and WMAP which gradually get improved and people keep re-using.

I just so far didnt see confidence intervals favoring the downside. Not really surprising either. And I am curious did anybody else?

===============

Nick thanks so much for the new paper! I will add it gratefully to my collection.

As far as I am concerned we are not arguing:smile: and this is partly repetitious. But here you have given me something new and I am glad!

Please explain it to me and interpret, if you so desire.

marcus

May20-06, 04:02 PM

this is an excellent one to add to the collection, thanks. It is from July 2005, so fairly recent though not the most so. Let's see what it says.
I am looking at Table 2, as you suggest. don't have time to study it at length but here's what I see it say:

the Omega_k error bar is around -0.074 with limits +0.049 and -0.052

so as I read it the error bar is between [-0.126, -0.025]

..

The nice paper Nick kindly provided is this one first posted July 2005

http://lanl.arxiv.org/abs/astro-ph/0507583
Cosmological parameters from CMB measurements and the final 2dFGRS power spectrum
Ariel G. Sanchez (Cordoba), C. M. Baugh (Durham), W. J. Percival (Edinburgh), J. A. Peacock (Edinburgh), N. D. Padilla (Catolica), S. Cole (Durham), C. S.Frenk (Durham), P. Norberg (ETH, Zurich)

MNRAS, in press. Minor revision after referee's report. 22 pages, 18 plots. Colour figures for talks (including additional plots which do not appear in the paper) can be downloaded from this http URL
Monthly Notices of the Roy.Astron.Soc. 366 (2006) 189-207

From Table 2 of this paper one gets a confidence interval for Omega_k
of [-0.126, -0.025]

this is the same all-negative interval situation that was so remarkable in Spergel at al, and seems to be yet another case of positive curvature---that is of Omega being on the upside of 1.

If one treats this Table 2 estimate the same way one treated Spergel, one gets this for Omega_total
[1.025, 1.126]

that is a little more marked than the Spergel WMAP3 thing of
[1.008, 1.037]

So far I dont see how this contradicts my general impression of how the papers keep leaning towards positive largescale curvature. I could very likely be missing something. Dont have time to study the whole paper and these damned minus signs and double negatives keep buzzing around like flies.

But anyway, I treat it exactly like I did Spergel et al, praying that they are using the same notation, and that's how it comes out.

SpaceTiger

May20-06, 11:44 PM

So far I dont see how this contradicts my general impression of how the papers keep leaning towards positive largescale curvature.

It doesn't, that's my mistake. The analysis actually includes the WMAP data (which is by far the strongest constraint on the curvature), so it would be surprising if it didn't end up leaning in the same direction.

OF COURSE THESE CONFIDENCE INTERVALS PEOPLE PUBLISH ARE NOT SEPARATE INDEPENDENT MEASUREMENTS, I am not doing statistics with them , THEY ARE ALL BASED ON THE SAME FEW DATASETS, like SDSS and WMAP which gradually get improved and people keep re-using.

Well, actually, some of them are independent (such as the Firmani et al. measurement you cited), so you'll have to be more precise about what you're thinking of when you say they all favor a closed universe. If most of the measurements you're thinking of are not independent, then I'm curious as to why you think they support your case. As you can see from Table 11 in the WMAP3 paper, all but one of the combined data sets brings the estimate on curvature down, suggesting that the high value of \Omega_{tot} comes primarily from the WMAP data...

marcus

May30-06, 08:08 PM

Hi all, here is another paper in the trail of fallout in the wake of WMAP3 that has to do with the closed universe issue.

http://arxiv.org/abs/astro-ph/0605709
How Many Universes Do There Need To Be?
Douglas Scott, J.P. Zibin
6 pages, 1 figure

"In the simplest cosmological models consistent with General Relativity, the total volume of the Universe is either finite or infinite, depending on whether or not the spatial curvature is positive. Current data suggest that the curvature is very close to flat, implying that one can place a lower limit on the total volume. In a Universe of finite age, the 'particle horizon' defines the patch of the Universe which is observable to us. Based on today's best-fit cosmological parameters it is possible to constrain the number of observable Universe sized patches, N_U. Specifically, using the new WMAP data, we can say that there are at least 10 patches out there the same volume as ours. Moreover, even if the precision of our cosmological measurements continues to increase, density perturbations at the particle horizon size limit us to never knowing that there are more than about 10^5 patches out there."

these people are at UBC Vancouver
douglas scott has 94 papers on arxiv mostly all published (all I saw were)
zibin has 5 up, all published, 4 co-authored with scott and one solo.
I don't know Scott by reputation, so I have to go by something and papers will do.
(some other authors mentioned on thread, such as Neil Cornish, i know from earlier
things so dont have to be so crude)

=================
so far what I am saying, all I can say, is something that doesnt officially MEAN anything. and that is the obviously true fact that so far, looking at published confidence intervals for Omega, what I PERSONALLY HAVE SEEN in my casual reading is either all on the upside of one, or if it brackets one, then it is quite noticeably overbalanced on the upside. This is more of the nature of an *odd fact* than anything else.

I PERSONALLY HAVE NOT SEEN and am still looking for an example of a paper that actually shows a confidence interval on the downside of one, or way leaning in that direction.

I would be delighted if anyone can show me a paper with that.

Meanwhile, we wait and keep casual track of the fallout as time and interest permits.

========================
hope everyone understands that I am not intending to "make a case" that the universe is closed or to argue that it is closed. I am a watcher of events in physics and cosmology and I anticipate a shift in the views of mainstream cosmologists. I expect it will take a while and may be shown by them becoming more open to considering various possibilities. I am waiting with some interest to see what happens.
I wonder, for example, if there will be more papers appearing like the one here by Scott and Zibin

this thread is not intended to persuade anyone of anything :smile: I am happy if everyone keeps their opinions exactly as they are! it is more of an observational thread, keeping track of the fall-out. Nobody is being encouraged to change their mind!

Chronos

May31-06, 02:03 AM

marcus

May31-06, 03:30 AM

The problem with 2df and SDSS, IMO, is z ~ 2 is pretty much the observational limit for 'ordinary' galaxies. With few exceptions, most are too faint to be observed much beyond z~1. AGN's, GRB's and likewise freakishly bright events are the only windows that remain observationally accessible. The puzzle box does not easily yield its secrets.

Chronos, I am delighted that you found the Scott and Zibin paper interesting enough to contribute a comment! I do not fully grasp the relevance of what you say to their paper (assuming you intend any) but I do readily acknowledge the difficulty of basing estimates of curvature, and of Omega, on ordinary galaxy counts.

fortunately, the Scott and Zibin paper is not based on galaxy counts, but on the microwave background. what they say is nice and clear and easy to remember.

they say look at the volume of the OBSERVABLE UNIVERSE, this is something that hellfire or others here could swiftly estimate as a certain number of cubic lightyears.

they say that they have learned from the WMAP3 data that THE VOLUME OF THE WHOLE UNIVERSE IS AT LEAST TEN TIMES LARGER THAN THE VOLUME OF THE OBSERVABLE UNIVERSE.

It might of course be infinity times larger, but at least it is TEN. that is sort of nice to know, is it not?

maybe I could do an OOM on the volume the current radius of the current observable is about 40 billion LY, so we just cube that ( 64,000 billion billion billion cubic LY) and multiply by 4 (which is the same as 4/3 pi) and we get 250 x 1030 cubic LY, anyway some large number like that: 2.5 x 1032 cubic LY.

the exact number doesnt matter. what Scott Zibin claim to show is that the total volume of the entire universe not just what we see but EVERYTHING---ALL THE SPACE THERE IS---is at least 10 times bigger volume than that. at the present moment of course, because that is when we are measuring and estimating.

it expandeth apace, so the volume will be larger in the future as result of expansion, but at the moment we know it is at least that large a volume---and of course it may be infinite.

Chronos

Jun1-06, 03:24 AM

Chronos, I am delighted that you found the Scott and Zibin paper interesting enough to contribute a comment! I do not fully grasp the relevance of what you say to their paper (assuming you intend any) but I do readily acknowledge the difficulty of basing estimates of curvature, and of Omega, on ordinary galaxy counts.

fortunately, the Scott and Zibin paper is not based on galaxy counts, but on the microwave background. what they say is nice and clear and easy to remember.My intent was to point out they conveniently ignored known galaxy counts [e.g., SDSS] and extrapolated a very speculative result.they say look at the volume of the OBSERVABLE UNIVERSE, this is something that hellfire or others here could swiftly estimate as a certain number of cubic lightyears.

they say that they have learned from the WMAP3 data that THE VOLUME OF THE WHOLE UNIVERSE IS AT LEAST TEN TIMES LARGER THAN THE VOLUME OF THE OBSERVABLE UNIVERSE.So what? These 'unobservable' universes sound like a 'landscape' to me. But, your point is clear. The gratuitious insult did not go unnoticed.It might of course be infinity times larger, but at least it is TEN. that is sort of nice to know, is it not?It is a nice speculation. I just disagree with the reasoning.
maybe I could do an OOM on the volume the current radius of the current observable is about 40 billion LY, so we just cube that ( 64,000 billion billion billion cubic LY) and multiply by 4 (which is the same as 4/3 pi) and we get 250 x 1030 cubic LY, anyway some large number like that: 2.5 x 1032 cubic LY.

the exact number doesnt matter. what Scott Zibin claim to show is that the total volume of the entire universe not just what we see but EVERYTHING---ALL THE SPACE THERE IS---is at least 10 times bigger volume than that. at the present moment of course, because that is when we are measuring and estimating.Circular reasoning is the first thought that comes to mind.

it expandeth apace, so the volume will be larger in the future as result of expansion, but at the moment we know it is at least that large a volume---and of course it may be infinite.

marcus

Jun1-06, 08:21 AM

**they say look at the volume of the OBSERVABLE UNIVERSE, this is something that hellfire or others here could swiftly estimate as a certain number of cubic lightyears.

they say that they have learned from the WMAP3 data that THE VOLUME OF THE WHOLE UNIVERSE IS AT LEAST TEN TIMES LARGER THAN THE VOLUME OF THE OBSERVABLE UNIVERSE.**

So what? These 'unobservable' universes sound like a 'landscape' to me. But, your point is clear. The gratuitious insult did not go unnoticed.

I'm baffled. No gratuitous insult was intended. What are you talking about? :smile:

To repeat, what the authors are attempting to do is to estimate a LOWER BOUND on the size of the universe.

Does anybody else think there is some problem with their lower bound?
Ought they have used other data, such as SDSS?

marcus

Aug1-06, 08:29 PM

http://arxiv.org/abs/astro-ph/0608017
Revised WMAP constraints on neutrino masses and other extensions of the minimal \LambdaCDM model
Jostein R. Kristiansen, Hans Kristian Eriksen, Oystein Elgaroy
7 pages, submitted to Physical Review D

my comment: Still chewing on the WMAP3 data. I like to sample papers every now and then to keep track.
Nothing really remarkable. I will get some exerpts.

===quote===

Data set Observations included
A WMAP
B WMAP + ACBAR + BOOMERanG
C WMAP + ACBAR + BOOMERanG + SDSS + 2dF + SNLS + HST + BBN + BAO
...
...

D. Spatial curvature

Next we add spatial curvature, \Omega_k to our sixparameter model. However, altering the geometry of universe mainly affects the positions of the CMB acoustic peaks, while the likelihood modifications mostly concern the amplitude and tilt of the power spectrum. A priori, one would therefore not expect any significant changes in \Omega_k. And as seen in Table V, this is indeed the case. For all data sets, \Omega_k = 0 is within about 1 sigma, in good agreement with the results from the WMAP team [1]. The large improvement of the limits on \Omega_k for data set C can to a large extent be understood by the well-known degeneracy between \Omega_k and h, where negative values of \Omega_k can be accommodated by a small h. I.e., when imposing the HST prior on h, the allowed range of \Omega_k is significantly constrained.

Data Set WMAP code Modified code

A -0.057 ^{+0.050}_{-0.056}[/tex] [itex] -0.057 ^{+0.050}_{-0.057}
- - -
B -0.056 ^{+0.052}_{-0.062} -0.055 ^{+0.048}_{-0.055}
- - -
C -0.005 +/-0.007 -0.006 +/-0.007

TABLE V: Estimated values for \Omega_k.

===endquote====

I've been having trouble getting this transcribed Table V to appear right and be legible. In any case I don't think it matters a lot. But as a sample if you look at case A, the confidence interval for the curvature omega is
[-0.113, -0.007]

that means the confidence interval for total Omega is [1.007, 1.113]
this is close enough to the flat case of Omega exactly equal to 1.000 so that one can say it is consistent with the picture of a spatially flat infinite universe

however as we've noticed before it is also consistent with Omega GREATER than 1, like for example 1.01 would actually be within the confidence interval. And that is consistent with the picture of a positive curved spatially FINITE universe. the term for that is "spatial closure"
the typical picture of a spatial slice would be a 3-sphere------like the familiar balloon 2-sphere except 3D instead of 2D
IT WOULD NOT MEAN A UNIVERSE THAT WILL DO A 'BIG CRUNCH' that kind of "closure" is a separate notion from spactial closure.

a spatial closed universe could expand forever----it is one possible version of the prevailing LambdaCDM model that cosmologists are using.

What I am interested in tracking in this thread is any sign of a shift in what cosmologists tacitly assume to be their typical LambdaCDM case. Do they typically assume spatial infinite (Omega = 1, flat) or do they assume
spatial closure (Omega > 1, "nearly flat" but slightly curved).

marcus

Aug29-06, 07:49 PM

Another episode in the Omega_total story
http://arxiv.org/abs/astro-ph/0608632
Cosmological Constraints from the SDSS Luminous Red Galaxies
M Tegmark, et al... [umpteen authors]
Comments: SDSS data and ppt figures available at this http URL 36 PRD pages, 25 figs

"We measure the large-scale real-space power spectrum P(k) using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmological parameters from the Wilkinson Microwave Anisotropy Probe (WMAP). ...
... Our results provide a striking confirmation of the predicted large-scale LCDM power spectrum. ...
...
... For LCDM, our power spectrum measurement improves the evidence for spatial flatness, sharpening the curvature constraint Omega=1.05+-0.05 from WMAP alone to Omega_tot=1.003+-0.010. All these constraints are essentially independent of scales k>0.1h/Mpc and associated nonlinear complications, yet agree well with more aggressive analyses where nonlinear modeling is crucial. (Abridged)"

Tegmark et al put it in this interval: [0.994, 1.013]
See their table 3, on page 14

WITHOUT the Sloan Digital Sky Survey, with WMAP ALONE they put it in the interval [1.008, 1.118]
again see table 3

See figures 16 and 17, around page 20. they graphically show how Tegmark et al NARROW DOWN the allowed Omega by supplementing WMAP data with SDSS and stellar ages.

=======always interesting to see how people talk========
Look around page 21

Although it has been argued that closed inflation models require particularly ugly fine-tuning [131], a number of recent papers have considered nearly-flat models either to explain the low CMB quadrupole [132], in string theory landscape-inspired short inflation models, or for anthropic reasons [108, 133, 134], so it is clearly interesting and worthwhile to continue sharpening observational tests of the flatness assumption. In the same spirit, measuring the Hubble parameter h independently of theoretical assumptions about curvature and measurements of galaxy distances at low redshift provides a powerful consistency check on our whole framework. Figures 15, 16 and 17 illustrate the well-known CMB degeneracies between the curvature...and dark energy ...,
the Hubble parameter h, and the age of the universe ...; without further information or priors, one cannot simultaneously demonstrate spatial flatness and accurately measure Omega_Lambda, h or t_now, since the CMB accurately constrains only the single combination.... Indeed, the WMAP3 degeneracy banana extends towards even larger Omega_total than these figures indicate; the plotted banana has been artificially truncated by a hardwired lower limit on h in the CosmoMC software...

So the slightly positive curved, spatially closed models are being called NEARLY FLAT. that is the term I need to keep an eye out for.
There is some reason that most researchers have preferred to consider the exactly flat case----the paper suggests some reasons having to do with "ugly fine-tuning the inflation"----and yet some other papers have chosen to consider this case: citations [132, 108, 133, 134]. One of these is a paper [108] which Tegmark wrote himself with Martin Rees.

So I would say, based on a brief inspection, that the paper still favors the flat case but that it has some portions which contemplate the NEARLY FLAT case.

marcus

Sep13-06, 07:32 PM

http://arxiv.org/abs/astro-ph/0609349
Was the universe open or closed before inflation?
Eduard Masso, Subhendra Mohanty, Gabriel Zsembinszki
5 pages, 3 figures
UAB-FT-609

"If the spatial curvature of the universe at the beginning of inflation is negative, there is an enhancement of the temperature anisotropy of the Cosmic Background Radiation at large angles. On the other hand if at the start of inflation the universe was closed with curvature there will be a suppression of temperature anisotropy at the scale of the present horizon. The observation of a low quadrupole anisotropy by WMAP suggests that the universe was closed with (\Omega-1) of order unity at the time when the perturbation scales of the size of our present horizon were exiting the inflationary horizon."

====exerpt=====
From the analyis of the three year WMAP data [2] it is concluded that a power power spectrum with an exponential cut-off at k_c/a_0 = 3 \times 10^{-4}Mpc^{-1} gives a better chi-square fit for the temperature anisotropy angular spectrum than the nearly scale invariant spectrum predicted by an generic slow roll inflation. If the universe was closed at the time of inflation then there is a natural cut-off of k^2 = K/a^2_i .
Running the cmbflat programme of CMBFAST [3] after modifying the primordial power spectrum of scalars by including the extra factor in the square brackets of (43), with \Omega_0 = 1
and other parameters as given by the central values of the λ CDM model, [2], we find that a good fit for the low-multipole TT anisotropy is obtained with |K|/(a_iH_{\lambda})^2 \sim 1 as shown in Fig.1. Therefore a natural explanation of the low cmb power at low l is that the universe was closed at the start of inflation with \Omega - 1 \sim O(1) .

marcus

Jan22-07, 08:51 PM

New Wright's new paper
just came out
http://arxiv.org/abs/astro-ph/0701584
discussion section page 14:

"Using all the data together
gives the plot shown in Figure 5. The best fit model is slightly closed with
Omega_tot = 1.011 and M = 0.315. "

Wright is an WMAP princ. investigator.

Here is Wright's paper

Constraints on Dark Energy from Supernovae, Gamma Ray Bursts, Acoustic Oscillations, Nucleosynthesis and Large Scale Structure and the Hubble constant
Edward L. Wright (UCLA)
16 pages, 8 figure

"The luminosity distance vs. redshift law is now measured using supernovae and gamma ray bursts, and the angular size distance is measured at the surface of last scattering by the CMB and at z = 0.35 by baryon acoustic oscillations. In this paper this data is fit to models for the equation of state with w = -1, w = const, and w(z) = w_0+w_a(1-a). The last model is poorly constrained by the distance data, leading to unphysical solutions where the dark energy dominates at early times unless the large scale structure and acoustic scale constraints are modified to allow for early time dark energy effects. A flat LambdaCDM model is consistent with all the data."

the initial announcement of WMAP3 "implications for cosmology" paper by Spergel et al already contained hint of this.
warning: it doesnt prove anything. the INFINITE FLAT universe is still consistent, it just is not the best fit. the best fit is with nearly spatially flat, slight positive spatial curvature and therefore the best fit is spatially finite.

flat would be Omega = 1.00 exactly, the best fit is Omega = 1.011

However as Ned Wright is careful to say: a flat model is "consistent" with the data

marcus

Feb26-07, 10:14 PM

noose is slowly tightening around the neck of the spatial flat universe assumption

couple of more papers

Bruce Basset et al
http://arxiv.org/abs/astro-ph/0702670
Dynamical Dark Energy or Simply Cosmic Curvature?
Chris Clarkson, Marina Cortes, Bruce A. Bassett
5 pages, 1 figure
"We show that the assumption of a flat universe induces critically large errors in reconstructing the dark energy equation of state at z>~0.9 even if the true cosmic curvature is very small, O(1%) or less. The spuriously reconstructed w(z) shows a range of unusual behaviour, including crossing of the phantom divide and mimicking of standard tracking quintessence models. For 1% curvature and LCDM, the error in w grows rapidly above z~0.9 reaching (50%,100%) by redshifts of (2.5,2.9) respectively, due to the long cosmological lever arm. Interestingly, the w(z) reconstructed from distance data and Hubble rate measurements have opposite trends due to the asymmetric influence of the curved geodesics. These results show that including curvature as a free parameter is imperative in any future analyses attempting to pin down the dynamics of dark energy, especially at moderate or high redshifts."

Joanna Dunkley et al
http://arxiv.org/abs/astro-ph/0507473
Measuring the geometry of the Universe in the presence of isocurvature modes
J. Dunkley, M. Bucher, P. G. Ferreira, K. Moodley, C. Skordis
4 pages, 5 figs.
Phys.Rev.Lett. 95 (2005) 261303

"The Cosmic Microwave Background (CMB) anisotropy constrains the geometry of the Universe because the positions of the acoustic peaks of the angular power spectrum depend strongly on the curvature of underlying three-dimensional space. In this Letter we exploit current observations to determine the spatial geometry of the Universe in the presence of isocurvature modes. Previous analyses have always assumed that the cosmological perturbations were initially adiabatic. A priori one might expect that allowing additional isocurvature modes would substantially degrade the constraints on the curvature of the Universe. We find, however, that if one considers additional data sets, the geometry remains well constrained. When the most general isocurvature perturbation is allowed, the CMB alone can only poorly constrain the geometry to Omega_0=1.6+-0.3. Including large-scale structure (LSS) data one obtains Omega_0=1.07+-0.03, and Omega_0=1.06+-0.02 when supplemented by the Hubble Space Telescope (HST) Key Project determination of H_0 and SNIa data."

The point is not whether you like flat or don't like flat. The point is we don't know and ASSUMING FLAT INTRODUCES ERRORS.. Assuming flat encourages circular reasoning (according to Ned Wright) and makes what you do unreliable. This is how Basset et al argue, and they cite Ned Wright too:
===quote Basset===
However, we will show that ignoring Omega_k induces errors in the reconstructed dark energy equation of state, w(z), that grow very rapidly with redshift and dominate the w(z) error budget at redshifts (z > 0.9) even if Omega_k is very small. The aim of this paper is to argue that future studies of dark energy, and in particular, of observational data, should include Omega_k as a parameter to be fitted alongside the w(z) parameters.

Looking back, this conclusion should not be unexpected. Firstly the case for flatness at the sub-percent level is not yet compelling: a general CDM analysis [13 the Dunkley paper], allowing for general correlated adiabatic and isocurvature perturbations, found that WMAP, together with largescale structure and HST Hubble constant constraints, yields
Omega_k = −0.06 ± 0.02.
We will show that significantly smaller values of Omega_k lead to large effects at redshifts z ~ 0.9 well within reach of the next generation of surveys.

Secondly, Wright (e.g.[14]) has petitioned hard against the circular logic that one can prove the joint statement (Omega_k = 0,w = −1) by simply proving the two conditional statements (Omega_k = 0 given that w = −1) and (w = −1 given that Omega_k = 0). ...

Given that the constraints on Omega_k evaporate precisely when w deviates most strongly from a cosmological constant, it is clearly inconsistent to assume Omega_k = 0 when deriving constraints on dynamical dark energy...
===endquote===